diff --git a/04_GrangerCausality/04_GrangerCausality.ipynb b/04_GrangerCausality/04_GrangerCausality.ipynb index 288e9f2..8f95754 100644 --- a/04_GrangerCausality/04_GrangerCausality.ipynb +++ b/04_GrangerCausality/04_GrangerCausality.ipynb @@ -6,20 +6,14 @@ "source": [ "# Chapter 4: Granger Causality Test\n", "\n", - "In the first three chapters, we discussed the classical methods for both univariate and multivariate time series forecasting. We now introduce the notion of causality and its implications on time series analysis in general. We also describe a test for the linear VAR model discussed in the previous chapter.\n", - "\n", - "Prepared by: Carlo Vincienzo G. Dajac" + "In the first three chapters, we discussed the classical methods for both univariate and multivariate time series forecasting. We now introduce the notion of causality and its implications on time series analysis in general. We also describe a test for the linear VAR model discussed in the previous chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**Chapter Outline**\n", - "* Notations\n", - "* Definitions\n", - "* Assunmptions\n", - "* Testing for Granger Causality" + "Prepared by: Carlo Vincienzo G. Dajac" ] }, { @@ -32,7 +26,7 @@ "\n", "Denote the optimum, unbiased, least-squares predictor of $A_t$ using the set of values $B_t$ by $P_t (A|B)$. Thus, for instance, $P_t (X|\\overline X)$ will be the optimum predictor of $X_t$ using only past $X_t$. The predictive error series will be denoted by $\\varepsilon_t(A|B) = A_t - P_t(A|B)$. Let $\\sigma^2 (A|B)$ be the variance of $\\varepsilon_t(A|B)$.\n", "\n", - "Let $U_t$ be all the information in the universe accumulated since time $t-1$ and let $U_t - Y_t$ denote all this information *apart* from the specified series $Y_t$." + "Let $U_t$ be all the information in the universe accumulated since time $t-1$ and let $U_t - Y_t$ denote all this information *apart* from the specified series $Y_t$, which is another stationary time series that is different from $X_t$." ] }, { @@ -41,10 +35,9 @@ "source": [ "## Definitions\n", "\n", - "\n", "### Causality\n", "\n", - "If $\\sigma^2 (X|U) < \\sigma^2 (X| \\overline{U-Y})$, we say that $Y$ is causing $X$, denoted by $Y_t \\implies X_t$. We say that $Y_t$ is causing $X_t$ if we are able to predict $X_t$ using all available information than if the information apart from $Y_t$ had been used.\n", + "If $\\sigma^2 (X|U) < \\sigma^2 (X| \\overline{U-Y})$, we say that $Y$ is causing $X$, denoted by $Y_t \\implies X_t$. We say that $Y_t$ is causing $X_t$ if we are **able to predict** $X_t$ using all available information than if the information apart from $Y_t$ had been used.\n", "\n", "### Feedback\n", "If $\\sigma^2 (X|\\overline U) < \\sigma^2 (X| \\overline{U-Y})$ and $\\sigma^2 (Y|\\overline U) < \\sigma^2 (Y| \\overline{U-X})$, we say that feedback is occurring, which is denoted by $Y_t \\iff X_t$, i.e., feedback is said to occur when $X_t$ is causing $Y_t$ and also $Y_t$ is causing $X_t$.\n", @@ -62,56 +55,48 @@ "source": [ "## Assumptions\n", "\n", - "* Series is stationary.\n", - "* Linear model is already optimized." + "* $X_t$ and $Y_t$ are stationary.\n", + "* $P_t (A|B)$ is already optimized." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Testing for Granger Causality" + "## Testing for Granger Causality\n", + "\n", + "We will be first building VAR models for our examples in this section. In addition to the steps outlined in the previous chapter, we will just call built-in Granger causality test function and configure it accordingly." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from pandas.plotting import lag_plot\n", + "from statsmodels.tsa.vector_ar.var_model import VAR\n", + "from statsmodels.tsa.stattools import adfuller, kpss, grangercausalitytests\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 1: Ipo Dam Dataset\n", + "\n", + "We will use the Ipo dataset in this example. It contains daily measurements of the following variables: rainfall (in millimeters), Oceanic Niño Index (ONI), NIA release flow (in cubic meters per second), and dam water level (in meters), respectively." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/Users/prince.javier/opt/anaconda3/lib/python3.7/site-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n", - " import pandas.util.testing as tm\n" - ] - } - ], - "source": [ - "import pandas as pd\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy import stats\n", - "from pandas.plotting import lag_plot\n", - "from statsmodels.tsa.api import VAR\n", - "from statsmodels.tsa.stattools import adfuller\n", - "from statsmodels.tsa.stattools import kpss\n", - "from statsmodels.tsa.stattools import grangercausalitytests\n", - "from statsmodels.tools.eval_measures import rmse, aic\n", - "from statsmodels.stats.stattools import durbin_watson" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We will use the Ipo dataset in this notebook." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, "outputs": [ { "data": { @@ -150,125 +135,105 @@ "
\n", "7116 rows × 4 columns
\n", "" ], "text/plain": [ - " Rain ONI NIA Dam\n", - "Time \n", - "0 0.00 -0.7 38.225693 100.70\n", - "1 0.00 -0.7 57.996530 100.63\n", - "2 0.00 -0.7 49.119213 100.56\n", - "3 0.00 -0.7 47.034720 100.55\n", - "4 0.00 -0.7 42.223380 100.48\n", - "... ... ... ... ...\n", - "7111 1.80 -0.2 5.040000 100.86\n", - "7112 1.60 -0.2 4.500000 101.01\n", - "7113 21.60 -0.2 6.730000 101.08\n", - "7114 0.20 -0.2 6.720000 100.92\n", - "7115 46.82 -0.2 1.950000 100.97\n", - "\n", - "[7116 rows x 4 columns]" + " Rain ONI NIA Dam\n", + "Time \n", + "0 0.0 -0.7 38.225693 100.70\n", + "1 0.0 -0.7 57.996530 100.63\n", + "2 0.0 -0.7 49.119213 100.56\n", + "3 0.0 -0.7 47.034720 100.55\n", + "4 0.0 -0.7 42.223380 100.48" ] }, - "execution_count": 3, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "data = pd.read_csv('../data/Ipo_dataset.csv', index_col='Time');\n", - "data = data.dropna()\n", - "data" + "ipo_df = pd.read_csv('../data/Ipo_dataset.csv', index_col='Time');\n", + "ipo_df = ipo_df.dropna()\n", + "ipo_df.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "7116 rows × 2 columns
\n", "" ], "text/plain": [ - " Rain Dam\n", - "Time \n", - "0 0.00 100.70\n", - "1 0.00 100.63\n", - "2 0.00 100.56\n", - "3 0.00 100.55\n", - "4 0.00 100.48\n", - "... ... ...\n", - "7111 1.80 100.86\n", - "7112 1.60 101.01\n", - "7113 21.60 101.08\n", - "7114 0.20 100.92\n", - "7115 46.82 100.97\n", - "\n", - "[7116 rows x 2 columns]" + " Rain Dam\n", + "Time \n", + "0 0.0 100.70\n", + "1 0.0 100.63\n", + "2 0.0 100.56\n", + "3 0.0 100.55\n", + "4 0.0 100.48" ] }, - "execution_count": 75, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "data = data.drop(['NIA', 'ONI'], axis=1)\n", - "data" + "data_df = ipo_df.drop(['ONI', 'NIA'], axis=1)\n", + "data_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**Step 1**: Test each time series for stationarity. Ideally, this should involve using a test (such as the ADF test) where the null hypothesis is non-stationarity, as well as a test (such as the KPSS test) where the null is stationarity. This is a good cross-check." + "We look at the lag plots to quickly check for stationarity." ] }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def lag_plots(data_df):\n", + " f, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 5))\n", + "\n", + " lag_plot(data_df[data_df.columns[0]], ax=ax1)\n", + " ax1.set_title(data_df.columns[0]);\n", + "\n", + " lag_plot(data_df[data_df.columns[1]], ax=ax2)\n", + " ax2.set_title(data_df.columns[1]);\n", + "\n", + " ax1.set_ylabel('$y_{t+1}$');\n", + " ax1.set_xlabel('$y_t$');\n", + " ax2.set_ylabel('$y_{t+1}$');\n", + " ax2.set_xlabel('$y_t$');\n", + "\n", + " plt.tight_layout()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ "\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.018 | \n", + "1.8045 | \n", + "
p-value | \n", + "0.100 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.6223 | \n", + "-5.8742 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0179 | \n", + "0.0047 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.6227 | \n", + "-21.5919 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "38.225693 | \n", + "100.70 | \n", + "
1 | \n", + "57.996530 | \n", + "100.63 | \n", + "
2 | \n", + "49.119213 | \n", + "100.56 | \n", + "
3 | \n", + "47.034720 | \n", + "100.55 | \n", + "
4 | \n", + "42.223380 | \n", + "100.48 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.184 | \n", + "1.8045 | \n", + "
p-value | \n", + "0.022 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-6.6030 | \n", + "-5.8742 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0048 | \n", + "0.0047 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-21.2837 | \n", + "-21.5919 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA_x | \n", + "Dam_x | \n", + "
---|---|---|
NIA_y | \n", + "1.0000 | \n", + "0.0007 | \n", + "
Dam_y | \n", + "0.0216 | \n", + "1.0000 | \n", + "
\n", + " | Rain | \n", + "ONI | \n", + "NIA | \n", + "Dam | \n", + "
---|---|---|---|---|
Time | \n", + "\n", + " | \n", + " | \n", + " | \n", + " |
0 | \n", + "0.0 | \n", + "-0.7 | \n", + "38.225693 | \n", + "78.63 | \n", + "
1 | \n", + "0.0 | \n", + "-0.7 | \n", + "57.996530 | \n", + "78.63 | \n", + "
2 | \n", + "0.0 | \n", + "-0.7 | \n", + "49.119213 | \n", + "78.61 | \n", + "
3 | \n", + "0.0 | \n", + "-0.7 | \n", + "47.034720 | \n", + "78.59 | \n", + "
4 | \n", + "0.0 | \n", + "-0.7 | \n", + "42.223380 | \n", + "78.56 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "0.0 | \n", + "78.63 | \n", + "
1 | \n", + "0.0 | \n", + "78.63 | \n", + "
2 | \n", + "0.0 | \n", + "78.61 | \n", + "
3 | \n", + "0.0 | \n", + "78.59 | \n", + "
4 | \n", + "0.0 | \n", + "78.56 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0327 | \n", + "1.8845 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.7136 | \n", + "-4.2004 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0007 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0327 | \n", + "0.0226 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.7138 | \n", + "-26.5948 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain_x | \n", + "Dam_x | \n", + "
---|---|---|
Rain_y | \n", + "1.0 | \n", + "0.0005 | \n", + "
Dam_y | \n", + "0.0 | \n", + "1.0000 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "38.225693 | \n", + "78.63 | \n", + "
1 | \n", + "57.996530 | \n", + "78.63 | \n", + "
2 | \n", + "49.119213 | \n", + "78.61 | \n", + "
3 | \n", + "47.034720 | \n", + "78.59 | \n", + "
4 | \n", + "42.223380 | \n", + "78.56 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.184 | \n", + "1.8845 | \n", + "
p-value | \n", + "0.022 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-6.6030 | \n", + "-4.2004 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0007 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0048 | \n", + "0.0226 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-21.2837 | \n", + "-26.5948 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "0.2295 | \n", + "0.3649 | \n", + "
p-value | \n", + "0.0100 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "-18.3281 | \n", + "-8.5824 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4304 | \n", + "-3.4304 | \n", + "
Critical value - 5% | \n", + "-2.8616 | \n", + "-2.8616 | \n", + "
Critical value - 10% | \n", + "-2.5668 | \n", + "-2.5668 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "0.0009 | \n", + "0.0024 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "-38.6219 | \n", + "-41.3374 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4304 | \n", + "-3.4304 | \n", + "
Critical value - 5% | \n", + "-2.8616 | \n", + "-2.8616 | \n", + "
Critical value - 10% | \n", + "-2.5668 | \n", + "-2.5668 | \n", + "
Given this, the general case of ARIMA(p,d,q) can be written as:
-Or in words :
@@ -478,35 +478,35 @@ X_{t} = \alpha _{1}X_{t-1} + \dots + \alpha _{p}X_{t-p} + \varepsilon _{t}+\thetBefore we discuss how we determine p, d, and q that are best to represent a time series, let’s first take a look at special cases of ARIMA models that should help us illustrate the formulation of the ARIMA equation.
Case 1: ARIMA(p,0,0) = autoregressive model: if the series is stationary and autocorrelated, perhaps it can be predicted as a multiple of its own previous value, plus a constant.
The forecasting equation for ARIMA(1,0,0) is:
-while ARIMA(2,0,0)
-or in general ARIMA(p,0,0)
-Case 2: ARIMA(0,0,q) = moving average model: if the series is stationary but is correlated to the errors of previous values, we can regress using the past forecast errors.
The forecasting equation for this is ARIMA(0,0,1) given by:
-or in simillar fashion to p, this can be generalized to ARIMA(0,0,q):
-where \(\theta_{q}\) is the coefficient at time \(t-q\) of the residual \(\varepsilon _{t-q}\).
Case 3: ARIMA(0,1,0) = Random Walk: if the series is non-stationary then the simplest model that we can use is a random walk model, which is given by:
-This can then further be generalized to ARIMA(0,d,0) simillar to the first two cases.
@@ -681,8 +681,8 @@ Critical Values: Dep. Variable: D.value No. Observations: 99 Model: ARIMA(2, 1, 3) Log Likelihood -251.701 Method: css-mle S.D. of innovations 3.050 -Date: Mon, 22 Feb 2021 AIC 517.402 -Time: 02:49:41 BIC 535.568 +Date: Wed, 24 Feb 2021 AIC 517.402 +Time: 14:54:10 BIC 535.568 Sample: 1 HQIC 524.752 ================================================================================= @@ -723,8 +723,8 @@ MA.3 -1.1296 +0.7624j 1.3628 0.4055 Dep. Variable: D.value No. Observations: 99 Model: ARIMA(1, 1, 1) Log Likelihood -253.790 Method: css-mle S.D. of innovations 3.119 -Date: Mon, 22 Feb 2021 AIC 515.579 -Time: 02:49:41 BIC 525.960 +Date: Wed, 24 Feb 2021 AIC 515.579 +Time: 14:54:11 BIC 525.960 Sample: 1 HQIC 519.779 ================================================================================= diff --git a/_build/html/02_LinearForecastingTrendandMomentumForecasting/02_LinearTrendandMomentumForecasting.html b/_build/html/02_LinearForecastingTrendandMomentumForecasting/02_LinearTrendandMomentumForecasting.html index 99b70f1..dd93ab4 100644 --- a/_build/html/02_LinearForecastingTrendandMomentumForecasting/02_LinearTrendandMomentumForecasting.html +++ b/_build/html/02_LinearForecastingTrendandMomentumForecasting/02_LinearTrendandMomentumForecasting.html @@ -769,7 +769,7 @@ lr confidence: 0.720499481096278<matplotlib.legend.Legend at 0x7fbc6a183a50>
+<matplotlib.legend.Legend at 0x7f9d05727610>
@@ -820,7 +820,7 @@ lr confidence: 0.720499481096278
[<matplotlib.lines.Line2D at 0x7fbc6a3d9290>]
+[<matplotlib.lines.Line2D at 0x7f9d06639950>]
@@ -840,7 +840,7 @@ lr confidence: 0.720499481096278
<matplotlib.legend.Legend at 0x7fbc6a425650>
+<matplotlib.legend.Legend at 0x7f9d06680250>
@@ -923,7 +923,7 @@ The mean absolute error, MAE is: 6.973973107834818
[<matplotlib.lines.Line2D at 0x7fbc6a0f38d0>]
+[<matplotlib.lines.Line2D at 0x7f9d056fbd90>]
@@ -1318,9 +1318,7 @@ The mean absolute error, MAE is: 6.973973107834818
Using Multivariate Linear Regression, we have the following equation:
-
CO2= 0.007805257527747128 x1 + 0.007550947270300682 x2 + 79.69471929115939
+CO2= 0.0078052575277471215 x1 + 0.007550947270300686 x2 + 79.6947192911594
array([95.05092409])
@@ -1341,7 +1339,7 @@ The mean absolute error, MAE is: 6.973973107834818
Mean Absolute Error: 5.670405502652304
+Mean Absolute Error: 5.670405502652306
Using Multivariate Linear Regression, we have the following equation:
-CO2= 0.00771675835477406 x1 + 0.007406759259298179 x2 + 80.02363225450095
+CO2= 0.007716758354774065 x1 + 0.007406759259298173 x2 + 80.02363225450095
Mean Absolute Error: 5.65574080048904
+Mean Absolute Error: 5.655740800489042
Using Multivariate Linear Regression, we have the following equation:
-CO2= 0.007019810017740837 x1 + 0.007728894654883428 x2 + 80.73020505101512
+CO2= 0.007019810017740837 x1 + 0.007728894654883425 x2 + 80.73020505101513
Mean Absolute Error: 5.610220319986727
+Mean Absolute Error: 5.610220319986732
Mean Absolute Error: 0.007450963714321594
+Mean Absolute Error: 0.0074509637143215
Mean Absolute Error: 0.11708568925420203
+Mean Absolute Error: 0.11708568925419785
The average Mean Absolute Error is for 730 sets of 24-hr data: 2.8599732777663385
+The average Mean Absolute Error is for 730 sets of 24-hr data: 2.859973277766325
<matplotlib.legend.Legend at 0x7fbc6aea7410>
+<matplotlib.legend.Legend at 0x7f9d0284ed10>
@@ -2254,7 +2252,7 @@ CO2= 0.007019810017740837 x1 + 0.007728894654883428 x2 + 80.73020505101512
<matplotlib.legend.Legend at 0x7fbc5080bf90>
+<matplotlib.legend.Legend at 0x7f9cec26c890>
@@ -2298,7 +2296,7 @@ CO2= 0.007019810017740837 x1 + 0.007728894654883428 x2 + 80.73020505101512
<matplotlib.legend.Legend at 0x7fbc50863110>
+<matplotlib.legend.Legend at 0x7f9cee5bb550>
@@ -2362,7 +2360,7 @@ CO2= 0.007019810017740837 x1 + 0.007728894654883428 x2 + 80.73020505101512
<matplotlib.legend.Legend at 0x7fbc50c988d0>
+<matplotlib.legend.Legend at 0x7f9cee823490>
diff --git a/_build/html/03_VectorAutoregressiveModels/03_VectorAutoregressiveMethods.html b/_build/html/03_VectorAutoregressiveModels/03_VectorAutoregressiveMethods.html
index 93b69c8..99b1757 100644
--- a/_build/html/03_VectorAutoregressiveModels/03_VectorAutoregressiveMethods.html
+++ b/_build/html/03_VectorAutoregressiveModels/03_VectorAutoregressiveMethods.html
@@ -964,113 +964,6 @@ This sample dataset contains weekly data of US Treasury rates from January 1982
- | p (mbar) | -T (degC) | -Tpot (K) | -Tdew (degC) | -rh (%) | -VPmax (mbar) | -VPact (mbar) | -VPdef (mbar) | -sh (g/kg) | -H2OC (mmol/mol) | -rho (g/m**3) | -wv (m/s) | -max. wv (m/s) | -wd (deg) | -
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Date Time | -- | - | - | - | - | - | - | - | - | - | - | - | - | - |
2009-01-01 00:10:00 | -996.52 | --8.02 | -265.40 | --8.90 | -93.3 | -3.33 | -3.11 | -0.22 | -1.94 | -3.12 | -1307.75 | -1.03 | -1.75 | -152.3 | -
2009-01-01 00:20:00 | -996.57 | --8.41 | -265.01 | --9.28 | -93.4 | -3.23 | -3.02 | -0.21 | -1.89 | -3.03 | -1309.80 | -0.72 | -1.50 | -136.1 | -
2009-01-01 00:30:00 | -996.53 | --8.51 | -264.91 | --9.31 | -93.9 | -3.21 | -3.01 | -0.20 | -1.88 | -3.02 | -1310.24 | -0.19 | -0.63 | -171.6 | -
where both \(y_{1,t}\) and \(y_{2,t}\) are assumed to be stationary, and \(\varepsilon_{1,t}\) and \(\varepsilon_{2,t}\) are the uncorrelated error terms with standard deviation \(\sigma_{1,t}\) and \(\sigma_{2,t}\), respectively.
In matrix notation: -
+Let -
+then
Let \(y_{1,t}\), \(y_{2,t}\) and \(y_{3,t}\) be the time series corresponding to CO signal, NO2 signal, and RH signal, respectively. Consider the moving average representation of the system shown below:
Let -
+Suppose \(u_1\) in the first equation increases by a value of one standard deviation.
This shock will change \(y_1\) in the current as well as the future periods.
In the first three chapters, we discussed the classical methods for both univariate and multivariate time series forecasting. We now introduce the notion of causality and its implications on time series analysis in general. We also describe a test for the linear VAR model discussed in the previous chapter.
Prepared by: Carlo Vincienzo G. Dajac
-Chapter Outline
-Notations
Definitions
Assunmptions
Testing for Granger Causality
If \(A_t\) is a stationary stochastic process, let \(\overline A_t\) represent the set of past values \({A_{t-j}, \; j=1,2,\ldots,\infty}\) and \(\overline{\overline A}_t\) represent the set of past and present values \({A_{t-j}, \; j=0,1,\ldots,\infty}\). Further, let \(\overline A(k)\) represent the set \({A_{t-j}, \; j=k,k+1,\ldots,\infty}\).
Denote the optimum, unbiased, least-squares predictor of \(A_t\) using the set of values \(B_t\) by \(P_t (A|B)\). Thus, for instance, \(P_t (X|\overline X)\) will be the optimum predictor of \(X_t\) using only past \(X_t\). The predictive error series will be denoted by \(\varepsilon_t(A|B) = A_t - P_t(A|B)\). Let \(\sigma^2 (A|B)\) be the variance of \(\varepsilon_t(A|B)\).
-Let \(U_t\) be all the information in the universe accumulated since time \(t-1\) and let \(U_t - Y_t\) denote all this information apart from the specified series \(Y_t\).
+Let \(U_t\) be all the information in the universe accumulated since time \(t-1\) and let \(U_t - Y_t\) denote all this information apart from the specified series \(Y_t\), which is another stationary time series that is different from \(X_t\).
If \(\sigma^2 (X|U) < \sigma^2 (X| \overline{U-Y})\), we say that \(Y\) is causing \(X\), denoted by \(Y_t \implies X_t\). We say that \(Y_t\) is causing \(X_t\) if we are able to predict \(X_t\) using all available information than if the information apart from \(Y_t\) had been used.
+If \(\sigma^2 (X|U) < \sigma^2 (X| \overline{U-Y})\), we say that \(Y\) is causing \(X\), denoted by \(Y_t \implies X_t\). We say that \(Y_t\) is causing \(X_t\) if we are able to predict \(X_t\) using all available information than if the information apart from \(Y_t\) had been used.
Series is stationary.
Linear model is already optimized.
\(X_t\) and \(Y_t\) are stationary.
\(P_t (A|B)\) is already optimized.
We will be first building VAR models for our examples in this section. In addition to the steps outlined in the previous chapter, we will just call built-in Granger causality test function and configure it accordingly.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
-from scipy import stats
from pandas.plotting import lag_plot
-from statsmodels.tsa.api import VAR
-from statsmodels.tsa.stattools import adfuller
-from statsmodels.tsa.stattools import kpss
-from statsmodels.tsa.stattools import grangercausalitytests
-from statsmodels.tools.eval_measures import rmse, aic
-from statsmodels.stats.stattools import durbin_watson
+from statsmodels.tsa.vector_ar.var_model import VAR
+from statsmodels.tsa.stattools import adfuller, kpss, grangercausalitytests
+import warnings
+warnings.filterwarnings("ignore")
We will use the Ipo dataset in this notebook.
+We will use the Ipo dataset in this example. It contains daily measurements of the following variables: rainfall (in millimeters), Oceanic Niño Index (ONI), NIA release flow (in cubic meters per second), and dam water level (in meters), respectively.
data = pd.read_csv('../data/Ipo_dataset.csv', index_col='Time');
-data = data.dropna()
-data
+ipo_df = pd.read_csv('../data/Ipo_dataset.csv', index_col='Time');
+ipo_df = ipo_df.dropna()
+ipo_df.head()
7116 rows × 4 columns
As an example, we will only use the NIA and Dam time series.
data = data.drop(['NIA', 'ONI'], axis=1)
-data
+fig,ax = plt.subplots(4, figsize=(15,8), sharex=True)
+plot_cols = ['Rain', 'ONI', 'NIA', 'Dam']
+ipo_df[plot_cols].plot(subplots=True, legend=False, ax=ax)
+for a in range(len(ax)):
+ ax[a].set_ylabel(plot_cols[a])
+ax[-1].set_xlabel('')
+plt.tight_layout()
+plt.show()
+
+
+
For this example, we will focus on the Rain and Dam time series.
+data_df = ipo_df.drop(['ONI', 'NIA'], axis=1)
+data_df.head()
7116 rows × 2 columns
Step 1: Test each time series for stationarity. Ideally, this should involve using a test (such as the ADF test) where the null hypothesis is non-stationarity, as well as a test (such as the KPSS test) where the null is stationarity. This is a good cross-check.
+We look at the lag plots to quickly check for stationarity.
f2, (ax4, ax5) = plt.subplots(1, 2, figsize=(15, 5))
-f2.tight_layout()
+def lag_plots(data_df):
+ f, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 5))
-lag_plot(data['Rain'], ax=ax4)
-ax4.set_title('Rainfall');
+ lag_plot(data_df[data_df.columns[0]], ax=ax1)
+ ax1.set_title(data_df.columns[0]);
-# lag_plot(data['NIA'], ax=ax4)
-# ax4.set_title('NIA Releases');
+ lag_plot(data_df[data_df.columns[1]], ax=ax2)
+ ax2.set_title(data_df.columns[1]);
-lag_plot(data['Dam'], ax=ax5)
-ax5.set_title('Dam Water Level');
+ ax1.set_ylabel('$y_{t+1}$');
+ ax1.set_xlabel('$y_t$');
+ ax2.set_ylabel('$y_{t+1}$');
+ ax2.set_xlabel('$y_t$');
-plt.show()
+ plt.tight_layout()
+
+
+
lag_plots(data_df)
Result: Both data are not stationary. We can make them stationary through differencing.
+Result: Dam does not look stationary. Rainfall lag plot is inconclusive.
+We use KPSS and ADF tests discussed in the previous chapter to conclusively check for stationarity.
# differencing for stationarity check
-rawData = data.copy(deep=True)
-
-# data['Rain'] = data['Rain'] - data['Rain'].shift(1)
-# data['NIA'] = data['NIA'] - data['NIA'].shift(1)
-data['Dam'] = data['Dam'] - data['Dam'].shift(1)
-data = data.dropna()
+def kpss_test(data_df):
+ test_stat, p_val = [], []
+ cv_1pct, cv_2p5pct, cv_5pct, cv_10pct = [], [], [], []
+ for c in data_df.columns:
+ kpss_res = kpss(data_df[c].dropna(), regression='ct')
+ test_stat.append(kpss_res[0])
+ p_val.append(kpss_res[1])
+ cv_1pct.append(kpss_res[3]['1%'])
+ cv_2p5pct.append(kpss_res[3]['2.5%'])
+ cv_5pct.append(kpss_res[3]['5%'])
+ cv_10pct.append(kpss_res[3]['10%'])
+ kpss_res_df = pd.DataFrame({'Test statistic': test_stat,
+ 'p-value': p_val,
+ 'Critical value - 1%': cv_1pct,
+ 'Critical value - 2.5%': cv_2p5pct,
+ 'Critical value - 5%': cv_5pct,
+ 'Critical value - 10%': cv_10pct},
+ index=data_df.columns).T
+ kpss_res_df = kpss_res_df.round(4)
+ return kpss_res_df
# split data into train and test sets for VAR later on
-end = round(len(data)*.8)
-train = data[:end]
-test = data[end:]
-
# ADF Null Hypothesis: there is a unit root, meaning series is non-stationary
-
-X1 = np.array(data['Dam'])
-X1 = X1[~np.isnan(X1)]
-
-result = adfuller(X1)
-print('ADF Statistic: %f' % result[0])
-print('p-value: %f' % result[1])
-print('Critical Values:')
-for key, value in result[4].items():
- print('\t%s: %.3f' % (key, value))
-
-
-X2 = np.array(data['Rain'])
-# X2 = np.array(data['NIA'])
-X2 = X2[~np.isnan(X2)]
-
-result = adfuller(X2)
-print('ADF Statistic: %f' % result[0])
-print('p-value: %f' % result[1])
-print('Critical Values:')
-for key, value in result[4].items():
- print('\t%s: %.3f' % (key, value))
+kpss_test(data_df)
ADF Statistic: -21.591918
-p-value: 0.000000
-Critical Values:
- 1%: -3.431
- 5%: -2.862
- 10%: -2.567
-ADF Statistic: -8.622738
-p-value: 0.000000
-Critical Values:
- 1%: -3.431
- 5%: -2.862
- 10%: -2.567
+
+
+
+
+
+
+ Rain
+ Dam
+
+
+
+
+ Test statistic
+ 0.018
+ 1.8045
+
+
+ p-value
+ 0.100
+ 0.0100
+
+
+ Critical value - 1%
+ 0.216
+ 0.2160
+
+
+ Critical value - 2.5%
+ 0.176
+ 0.1760
+
+
+ Critical value - 5%
+ 0.146
+ 0.1460
+
+
+ Critical value - 10%
+ 0.119
+ 0.1190
+
+
+
+
Result: Rain is stationary, while Dam is not.
+def adf_test(data_df):
+ test_stat, p_val = [], []
+ cv_1pct, cv_5pct, cv_10pct = [], [], []
+ for c in data_df.columns:
+ adf_res = adfuller(data_df[c].dropna())
+ test_stat.append(adf_res[0])
+ p_val.append(adf_res[1])
+ cv_1pct.append(adf_res[4]['1%'])
+ cv_5pct.append(adf_res[4]['5%'])
+ cv_10pct.append(adf_res[4]['10%'])
+ adf_res_df = pd.DataFrame({'Test statistic': test_stat,
+ 'p-value': p_val,
+ 'Critical value - 1%': cv_1pct,
+ 'Critical value - 5%': cv_5pct,
+ 'Critical value - 10%': cv_10pct},
+ index=data_df.columns).T
+ adf_res_df = adf_res_df.round(4)
+ return adf_res_df
# KPSS Null Hypothesis: there is no unit root, meaning series is stationary
-
-def kpss_test(series, **kw):
- statistic, p_value, n_lags, critical_values = kpss(series, **kw)
- # Format Output
- print(f'KPSS Statistic: {statistic}')
- print(f'p-value: {p_value}')
- print(f'num lags: {n_lags}')
- print('Critial Values:')
- for key, value in critical_values.items():
- print(f' {key} : {value}')
- print(f'Result: The series is {"not " if p_value < 0.05 else ""}stationary')
-
-kpss_test(X1)
-kpss_test(X2)
+adf_test(data_df)
KPSS Statistic: 0.009242367643647224
-p-value: 0.1
-num lags: 35
-Critial Values:
- 10% : 0.347
- 5% : 0.463
- 2.5% : 0.574
- 1% : 0.739
-Result: The series is stationary
-KPSS Statistic: 0.09395749653745288
-p-value: 0.1
-num lags: 35
-Critial Values:
- 10% : 0.347
- 5% : 0.463
- 2.5% : 0.574
- 1% : 0.739
-Result: The series is stationary
-
/Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages/statsmodels/tsa/stattools.py:1875: FutureWarning: The behavior of using nlags=None will change in release 0.13.Currently nlags=None is the same as nlags="legacy", and so a sample-size lag length is used. After the next release, the default will change to be the same as nlags="auto" which uses an automatic lag length selection method. To silence this warning, either use "auto" or "legacy"
- warnings.warn(msg, FutureWarning)
-/Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages/statsmodels/tsa/stattools.py:1911: InterpolationWarning: The test statistic is outside of the range of p-values available in the
-look-up table. The actual p-value is greater than the p-value returned.
+
+
+
+
+
+
+ Rain
+ Dam
+
+
+
+
+ Test statistic
+ -8.6223
+ -5.8742
+
+
+ p-value
+ 0.0000
+ 0.0000
+
+
+ Critical value - 1%
+ -3.4313
+ -3.4313
+
+
+ Critical value - 5%
+ -2.8619
+ -2.8619
+
+
+ Critical value - 10%
+ -2.5670
+ -2.5670
+
+
+
+
Results: ADF Null Hypothesis is rejected. Thus, data is stationary. KPSS Null Hypothesis could not be rejected. Thus, data is stationary.
+Result: Both data are stationary.
+Since both the lag plot and KPSS test indicate that Dam is not stationary, we apply differencing first before building our VAR model.
f2, (ax4, ax5) = plt.subplots(1, 2, figsize=(15, 5))
-f2.tight_layout()
-
-lag_plot(data['Rain'], ax=ax4)
-ax4.set_title('Rainfall');
-
-# lag_plot(data['NIA'], ax=ax4)
-# ax4.set_title('NIA Releases');
-
-lag_plot(data['Dam'], ax=ax5)
-ax5.set_title('Dam Water Level');
-
-plt.show()
+data_df['Dam'] = data_df['Dam'] - data_df['Dam'].shift(1)
+data_df = data_df.dropna()
+
+
+
We again look at the lag plots and apply the KPSS and ADF tests.
+lag_plots(data_df)
Result: Lag plots confirm results of ADF test and KPSS test.
-Step 2: Set up a VAR model for the data (without differencing).
model = VAR(train)
-model_fitted = model.fit(2)
+kpss_test(data_df)
/Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:579: ValueWarning: An unsupported index was provided and will be ignored when e.g. forecasting.
- ' ignored when e.g. forecasting.', ValueWarning)
-
Step 4: Make sure that the VAR is well-specified. For example, ensure that there is no serial correlation in the residuals. If need be, increase p until any autocorrelation issues are resolved.
-#Check for Serial Correlation of Residuals (Errors) using Durbin Watson Statistic
-#The value of this statistic can vary between 0 and 4.
-#The closer it is to the value 2, then there is no significant serial correlation.
-#The closer to 0, there is a positive serial correlation,
-#and the closer it is to 4 implies negative serial correlation.
+
+
+
+
+
+
+ Rain
+ Dam
+
+
+
+
+ Test statistic
+ 0.0179
+ 0.0047
+
+
+ p-value
+ 0.1000
+ 0.1000
+
+
+ Critical value - 1%
+ 0.2160
+ 0.2160
+
+
+ Critical value - 2.5%
+ 0.1760
+ 0.1760
+
+
+ Critical value - 5%
+ 0.1460
+ 0.1460
+
+
+ Critical value - 10%
+ 0.1190
+ 0.1190
+
+
+
+
adf_test(data_df)
Rain : 2.01
-Dam : 2.07
+
+
+
+
+
+
+ Rain
+ Dam
+
+
+
+
+ Test statistic
+ -8.6227
+ -21.5919
+
+
+ p-value
+ 0.0000
+ 0.0000
+
+
+ Critical value - 1%
+ -3.4313
+ -3.4313
+
+
+ Critical value - 5%
+ -2.8619
+ -2.8619
+
+
+ Critical value - 10%
+ -2.5670
+ -2.5670
+
+
+
+
Result: All three conclusively agree that both data are now stationary.
+We next split the data into train and test sets for the VAR model.
+def splitter(data_df):
+ end = round(len(data_df)*.8)
+ train_df = data_df[:end]
+ test_df = data_df[end:]
+ return train_df, test_df
Result: There is no significant correlation between in the residuals.
-Step 5: Now take the preferred VAR model and add in m additional lags of each of the variables into each of the equations.
model = VAR(train)
-model_fitted = model.fit(2)
-#get the lag order
-lag_order = model_fitted.k_ar
-print(lag_order)
+train_df, test_df = splitter(data_df)
+
+
+
We then select the VAR order \(p\) by computing the different multivariate information criteria (AIC, BIC, HQIC), and FPE.
+def select_p(train_df):
+ aic, bic, fpe, hqic = [], [], [], []
+ model = VAR(train_df)
+ p = np.arange(1,60)
+ for i in p:
+ result = model.fit(i)
+ aic.append(result.aic)
+ bic.append(result.bic)
+ fpe.append(result.fpe)
+ hqic.append(result.hqic)
+ lags_metrics_df = pd.DataFrame({'AIC': aic,
+ 'BIC': bic,
+ 'HQIC': hqic,
+ 'FPE': fpe},
+ index=p)
+ fig, ax = plt.subplots(1, 4, figsize=(15, 3), sharex=True)
+ lags_metrics_df.plot(subplots=True, ax=ax, marker='o')
+ plt.tight_layout()
+ print(lags_metrics_df.idxmin(axis=0))
+
select_p(train_df)
2
+AIC 21
+BIC 8
+HQIC 11
+FPE 21
+dtype: int64
-/Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:579: ValueWarning: An unsupported index was provided and will be ignored when e.g. forecasting.
- ' ignored when e.g. forecasting.', ValueWarning)
-
+
Step 6: Test for Granger non-causality.
+Result: We see that BIC has the lowest value at \(p=8\) while HQIC at \(p=11\). Although both AIC and FPE have the lowest value at \(p=21\), their plots also show an elbow. We can thus select the number of lags to be 8 (also for computational efficiency).
+We now fit the VAR model with the chosen order.
maxlag = lag_order
-test = 'ssr_chi2test'
-def grangers_causation_matrix(data, variables, test='ssr_chi2test', verbose=False):
+p = 8
+model = VAR(train_df)
+var_model = model.fit(p)
+
+
+
We can finally test the variables for Granger Causality
+def granger_causation_matrix(data, variables, p, test = 'ssr_chi2test', verbose=False):
"""Check Granger Causality of all possible combinations of the time series.
- The rows are the response variable, columns are predictors. The values in the table
+ The rows are the response variables, columns are predictors. The values in the table
are the P-Values. P-Values lesser than the significance level (0.05), implies
the Null Hypothesis that the coefficients of the corresponding past values is
zero, that is, the X does not cause Y can be rejected.
@@ -869,23 +1048,21 @@ Dam : 2.07
df = pd.DataFrame(np.zeros((len(variables), len(variables))), columns=variables, index=variables)
for c in df.columns:
for r in df.index:
- test_result = grangercausalitytests(data[[r, c]], maxlag=maxlag, verbose=False)
- p_values = [round(test_result[i+1][0][test][1],4) for i in range(maxlag)]
+ test_result = grangercausalitytests(data[[r, c]], p, verbose=False)
+ p_values = [round(test_result[i+1][0][test][1],4) for i in range(p)]
if verbose: print(f'Y = {r}, X = {c}, P Values = {p_values}')
min_p_value = np.min(p_values)
df.loc[r, c] = min_p_value
df.columns = [var + '_x' for var in variables]
df.index = [var + '_y' for var in variables]
return df
-
-o = grangers_causation_matrix(train, variables = train.columns)
o
+granger_causation_matrix(train_df, train_df.columns, p)
Result: If a given p-value is < significance level (0.05), then, the corresponding X series (column) causes the Y (row).
-For this particular example, we can say that NIA releases causes changes in the dam water level. On the other hand, dam water level also causes changes in the NIA releases. This is an example of the feedback mentioned above.
-We do the similar steps for the La Mesa dataset.
+Recall: If a given p-value is < significance level (0.05), then, the corresponding X series (column) causes the Y (row).
+Results: For this particular example, we can say that rainfall Granger causes changes in the dam water level. This means that rainfall data improves changes in dam water level prediction performance.
+On the other hand, changes in dam water level does not Granger cause rainfall. This means that changes in dam water level data does not improve rainfall prediction performance.
+ +In this next example, we now focus on the NIA and Dam time series.
data = pd.read_csv('../data/La Mesa_dataset.csv', index_col='Time');
-data = data.dropna()
-data = data.drop(['Rain', 'ONI'], axis=1)
-# data['Rain'] = data['Rain'] - data['Rain'].shift(1)
-data['NIA'] = data['NIA'] - data['NIA'].shift(1)
-data['Dam'] = data['Dam'] - data['Dam'].shift(1)
-data = data.dropna()
-
-train = data[:end]
-test = data[end:]
-
-model = VAR(train)
-model_fitted = model.fit(2)
-lag_order = model_fitted.k_ar
-
-maxlag = lag_order
-test = 'ssr_chi2test'
-
-o1 = grangers_causation_matrix(train, variables = train.columns)
-o1
+data_df = ipo_df.drop(['ONI', 'Rain'], axis=1)
+data_df.head()
/Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:579: ValueWarning: An unsupported index was provided and will be ignored when e.g. forecasting.
- ' ignored when e.g. forecasting.', ValueWarning)
+
+
+
+
+
+
+ NIA
+ Dam
+
+
+ Time
+
+
+
+
+
+
+ 0
+ 38.225693
+ 100.70
+
+
+ 1
+ 57.996530
+ 100.63
+
+
+ 2
+ 49.119213
+ 100.56
+
+
+ 3
+ 47.034720
+ 100.55
+
+
+ 4
+ 42.223380
+ 100.48
+
+
+
+
We first check for stationarity by looking at the lag plots and applying the KPSS and ADF tests.
+lag_plots(data_df)
kpss_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +0.184 | +1.8045 | +
p-value | +0.022 | +0.0100 | +
Critical value - 1% | +0.216 | +0.2160 | +
Critical value - 2.5% | +0.176 | +0.1760 | +
Critical value - 5% | +0.146 | +0.1460 | +
Critical value - 10% | +0.119 | +0.1190 | +
adf_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +-6.6030 | +-5.8742 | +
p-value | +0.0000 | +0.0000 | +
Critical value - 1% | +-3.4313 | +-3.4313 | +
Critical value - 5% | +-2.8619 | +-2.8619 | +
Critical value - 10% | +-2.5670 | +-2.5670 | +
Result: All three conclusively show that both data are not stationary.
+We apply differencing and recheck for stationarity.
+data_df['NIA'] = data_df['NIA'] - data_df['NIA'].shift(1)
+data_df['Dam'] = data_df['Dam'] - data_df['Dam'].shift(1)
+data_df = data_df.dropna()
+
lag_plots(data_df)
+
kpss_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +0.0048 | +0.0047 | +
p-value | +0.1000 | +0.1000 | +
Critical value - 1% | +0.2160 | +0.2160 | +
Critical value - 2.5% | +0.1760 | +0.1760 | +
Critical value - 5% | +0.1460 | +0.1460 | +
Critical value - 10% | +0.1190 | +0.1190 | +
adf_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +-21.2837 | +-21.5919 | +
p-value | +0.0000 | +0.0000 | +
Critical value - 1% | +-3.4313 | +-3.4313 | +
Critical value - 5% | +-2.8619 | +-2.8619 | +
Critical value - 10% | +-2.5670 | +-2.5670 | +
Result: All three conclusively agree that both data are now stationary.
+We next split the data and select the lag order \(p\).
+train_df, test_df = splitter(data_df)
+
select_p(train_df)
+
AIC 27
+BIC 8
+HQIC 13
+FPE 27
+dtype: int64
+
We select \(p=8\) with the same reasons as before. We finally fit our VAR model and test for Granger Causality.
+p = 8
+model = VAR(train_df)
+var_model = model.fit(p)
+
granger_causation_matrix(train_df, train_df.columns, p)
+
+ | NIA_x | +Dam_x | +
---|---|---|
NIA_y | +1.0000 | +0.0007 | +
Dam_y | +0.0216 | +1.0000 | +
Recall: If a given p-value is < significance level (0.05), then, the corresponding X series (column) causes the Y (row).
+Result: For this particular example, we can say that changes in NIA release flow Granger causes changes in the dam water level. Conversely, changes in dam water level also Granger causes changes in the NIA release flow. This is an example of the feedback mentioned in an earlier section above. This means that NIA release flow data improves changes in dam water level prediction performance, and dam water level data also improves changes in NIA release flow prediction performance.
+We now do the same steps for the La Mesa dataset.
+lamesa_df = pd.read_csv('../data/La Mesa_dataset.csv', index_col='Time');
+lamesa_df = lamesa_df.dropna()
+lamesa_df.head()
+
+ | Rain | +ONI | +NIA | +Dam | +
---|---|---|---|---|
Time | ++ | + | + | + |
0 | +0.0 | +-0.7 | +38.225693 | +78.63 | +
1 | +0.0 | +-0.7 | +57.996530 | +78.63 | +
2 | +0.0 | +-0.7 | +49.119213 | +78.61 | +
3 | +0.0 | +-0.7 | +47.034720 | +78.59 | +
4 | +0.0 | +-0.7 | +42.223380 | +78.56 | +
fig,ax = plt.subplots(4, figsize=(15,8), sharex=True)
+plot_cols = ['Rain', 'ONI', 'NIA', 'Dam']
+lamesa_df[plot_cols].plot(subplots=True, legend=False, ax=ax)
+for a in range(len(ax)):
+ ax[a].set_ylabel(plot_cols[a])
+ax[-1].set_xlabel('')
+plt.tight_layout()
+plt.show()
+
In this next example, we first consider the Rain and Dam time series.
+data_df = lamesa_df.drop(['ONI', 'NIA'], axis=1)
+data_df.head()
+
+ | Rain | +Dam | +
---|---|---|
Time | ++ | + |
0 | +0.0 | +78.63 | +
1 | +0.0 | +78.63 | +
2 | +0.0 | +78.61 | +
3 | +0.0 | +78.59 | +
4 | +0.0 | +78.56 | +
We first check for stationarity by looking at the lag plots and applying the KPSS and ADF tests.
+lag_plots(data_df)
+
kpss_test(data_df)
+
+ | Rain | +Dam | +
---|---|---|
Test statistic | +0.0327 | +1.8845 | +
p-value | +0.1000 | +0.0100 | +
Critical value - 1% | +0.2160 | +0.2160 | +
Critical value - 2.5% | +0.1760 | +0.1760 | +
Critical value - 5% | +0.1460 | +0.1460 | +
Critical value - 10% | +0.1190 | +0.1190 | +
adf_test(data_df)
+
+ | Rain | +Dam | +
---|---|---|
Test statistic | +-8.7136 | +-4.2004 | +
p-value | +0.0000 | +0.0007 | +
Critical value - 1% | +-3.4313 | +-3.4313 | +
Critical value - 5% | +-2.8619 | +-2.8619 | +
Critical value - 10% | +-2.5670 | +-2.5670 | +
Result: All three conclusively show that again Rain is stationary, while Dam is not.
+We apply differencing and recheck for stationarity.
+data_df['Dam'] = data_df['Dam'] - data_df['Dam'].shift(1)
+data_df = data_df.dropna()
+
lag_plots(data_df)
+
kpss_test(data_df)
+
+ | Rain | +Dam | +
---|---|---|
Test statistic | +0.0327 | +0.0226 | +
p-value | +0.1000 | +0.1000 | +
Critical value - 1% | +0.2160 | +0.2160 | +
Critical value - 2.5% | +0.1760 | +0.1760 | +
Critical value - 5% | +0.1460 | +0.1460 | +
Critical value - 10% | +0.1190 | +0.1190 | +
adf_test(data_df)
+
+ | Rain | +Dam | +
---|---|---|
Test statistic | +-8.7138 | +-26.5948 | +
p-value | +0.0000 | +0.0000 | +
Critical value - 1% | +-3.4313 | +-3.4313 | +
Critical value - 5% | +-2.8619 | +-2.8619 | +
Critical value - 10% | +-2.5670 | +-2.5670 | +
Result: All three conclusively agree that both data are now stationary.
+We next split the data and select the lag order \(p\).
+train_df, test_df = splitter(data_df)
+
select_p(train_df)
+
AIC 7
+BIC 6
+HQIC 7
+FPE 7
+dtype: int64
+
We select \(p=7\). We finally fit our VAR model and test for Granger Causality.
+p = 7
+model = VAR(train_df)
+var_model = model.fit(p)
+
granger_causation_matrix(train_df, train_df.columns, p)
+
+ | Rain_x | +Dam_x | +
---|---|---|
Rain_y | +1.0 | +0.0005 | +
Dam_y | +0.0 | +1.0000 | +
Recall: If a given p-value is < significance level (0.05), then, the corresponding X series (column) causes the Y (row).
+Result: For this particular example, we can say that rainfall Granger causes changes in the dam water level. Conversely, changes in dam water level also Granger causes rainfall. This is another example of feedback. This means that rainfall data improves changes in dam water level prediction performance, and dam water level data also improves rainfall prediction performance.
+In this next example, we now focus on the NIA and Dam time series.
+data_df = lamesa_df.drop(['ONI', 'Rain'], axis=1)
+data_df.head()
+
+ | NIA | +Dam | +
---|---|---|
Time | ++ | + |
0 | +38.225693 | +78.63 | +
1 | +57.996530 | +78.63 | +
2 | +49.119213 | +78.61 | +
3 | +47.034720 | +78.59 | +
4 | +42.223380 | +78.56 | +
We first check for stationarity by looking at the lag plots and applying the KPSS and ADF tests.
+lag_plots(data_df)
+
kpss_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +0.184 | +1.8845 | +
p-value | +0.022 | +0.0100 | +
Critical value - 1% | +0.216 | +0.2160 | +
Critical value - 2.5% | +0.176 | +0.1760 | +
Critical value - 5% | +0.146 | +0.1460 | +
Critical value - 10% | +0.119 | +0.1190 | +
adf_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +-6.6030 | +-4.2004 | +
p-value | +0.0000 | +0.0007 | +
Critical value - 1% | +-3.4313 | +-3.4313 | +
Critical value - 5% | +-2.8619 | +-2.8619 | +
Critical value - 10% | +-2.5670 | +-2.5670 | +
Result: All three conclusively show that both data are not stationary.
+We apply differencing and recheck for stationarity.
+data_df['NIA'] = data_df['NIA'] - data_df['NIA'].shift(1)
+data_df['Dam'] = data_df['Dam'] - data_df['Dam'].shift(1)
+data_df = data_df.dropna()
+
lag_plots(data_df)
+
kpss_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +0.0048 | +0.0226 | +
p-value | +0.1000 | +0.1000 | +
Critical value - 1% | +0.2160 | +0.2160 | +
Critical value - 2.5% | +0.1760 | +0.1760 | +
Critical value - 5% | +0.1460 | +0.1460 | +
Critical value - 10% | +0.1190 | +0.1190 | +
adf_test(data_df)
+
+ | NIA | +Dam | +
---|---|---|
Test statistic | +-21.2837 | +-26.5948 | +
p-value | +0.0000 | +0.0000 | +
Critical value - 1% | +-3.4313 | +-3.4313 | +
Critical value - 5% | +-2.8619 | +-2.8619 | +
Critical value - 10% | +-2.5670 | +-2.5670 | +
Result: All three conclusively agree that both data are now stationary.
+We next split the data and select the lag order \(p\).
+train_df, test_df = splitter(data_df)
+
select_p(train_df)
+
AIC 14
+BIC 2
+HQIC 8
+FPE 14
+dtype: int64
+
We select \(p=14\). We finally fit our VAR model and test for Granger Causality.
+p = 14
+model = VAR(train_df)
+var_model = model.fit(p)
+
granger_causation_matrix(train_df, train_df.columns, p)
+
+ | p (mbar) | +T (degC) | +
---|---|---|
Test statistic | +0.2295 | +0.3649 | +
p-value | +0.0100 | +0.0100 | +
Critical value - 1% | +0.2160 | +0.2160 | +
Critical value - 2.5% | +0.1760 | +0.1760 | +
Critical value - 5% | +0.1460 | +0.1460 | +
Critical value - 10% | +0.1190 | +0.1190 |
f2, (ax4, ax5) = plt.subplots(1, 2, figsize=(15, 5))
-f2.tight_layout()
-
-lag_plot(jena_sample['p (mbar)'], ax=ax4)
-ax4.set_title('p (mbar)');
-
-lag_plot(jena_sample['T (degC)'], ax=ax5)
-ax5.set_title('T (degC)');
-
-plt.show()
+adf_test(data_df)
+ | p (mbar) | +T (degC) | +
---|---|---|
Test statistic | +-18.3281 | +-8.5824 | +
p-value | +0.0000 | +0.0000 | +
Critical value - 1% | +-3.4304 | +-3.4304 | +
Critical value - 5% | +-2.8616 | +-2.8616 | +
Critical value - 10% | +-2.5668 | +-2.5668 | +
Result: T data is not stationary. We use differencing to make it stationary.
+Result: All three conclusively show that both data are not stationary.
+We apply differencing and recheck for stationarity.
# differencing for stationarity check
-rawData = jena_sample.copy(deep=True)
-
-jena_sample['p (mbar)'] = jena_sample['p (mbar)'] - jena_sample['p (mbar)'].shift(1)
-jena_sample['T (degC)'] = jena_sample['T (degC)'] - jena_sample['T (degC)'].shift(1)
-jena_sample = jena_sample.dropna()
+data_df['p (mbar)'] = data_df['p (mbar)'] - data_df['p (mbar)'].shift(1)
+data_df['T (degC)'] = data_df['T (degC)'] - data_df['T (degC)'].shift(1)
+data_df = data_df.dropna()
+
+
+
lag_plots(data_df)
<ipython-input-98-3aed1e4c60a7>:4: SettingWithCopyWarning:
-A value is trying to be set on a copy of a slice from a DataFrame.
-Try using .loc[row_indexer,col_indexer] = value instead
-
-See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
- jena_sample['p (mbar)'] = jena_sample['p (mbar)'] - jena_sample['p (mbar)'].shift(1)
-<ipython-input-98-3aed1e4c60a7>:5: SettingWithCopyWarning:
-A value is trying to be set on a copy of a slice from a DataFrame.
-Try using .loc[row_indexer,col_indexer] = value instead
-
-See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
- jena_sample['T (degC)'] = jena_sample['T (degC)'] - jena_sample['T (degC)'].shift(1)
-
# split data into train and test sets for VAR later on
-end = round(len(jena_sample)*.8)
-train = jena_sample[:end]
-test = jena_sample[end:]
-
# ADF Null Hypothesis: there is a unit root, meaning series is non-stationary
-
-X1 = np.array(jena_sample['p (mbar)'])
-X1 = X1[~np.isnan(X1)]
-
-result = adfuller(X1)
-print('ADF Statistic: %f' % result[0])
-print('p-value: %f' % result[1])
-print('Critical Values:')
-for key, value in result[4].items():
- print('\t%s: %.3f' % (key, value))
-
-
-X2 = np.array(jena_sample['T (degC)'])
-X2 = X2[~np.isnan(X2)]
-
-result = adfuller(X2)
-print('ADF Statistic: %f' % result[0])
-print('p-value: %f' % result[1])
-print('Critical Values:')
-for key, value in result[4].items():
- print('\t%s: %.3f' % (key, value))
+kpss_test(data_df)
ADF Statistic: -59.104716
-p-value: 0.000000
-Critical Values:
- 1%: -3.430
- 5%: -2.862
- 10%: -2.567
-ADF Statistic: -122.256393
-p-value: 0.000000
-Critical Values:
- 1%: -3.430
- 5%: -2.862
- 10%: -2.567
-
+ | p (mbar) | +T (degC) | +
---|---|---|
Test statistic | +0.0009 | +0.0024 | +
p-value | +0.1000 | +0.1000 | +
Critical value - 1% | +0.2160 | +0.2160 | +
Critical value - 2.5% | +0.1760 | +0.1760 | +
Critical value - 5% | +0.1460 | +0.1460 | +
Critical value - 10% | +0.1190 | +0.1190 | +
# KPSS Null Hypothesis: there is no unit root, meaning series is stationary
-
-def kpss_test(series, **kw):
- statistic, p_value, n_lags, critical_values = kpss(series, **kw)
- # Format Output
- print(f'KPSS Statistic: {statistic}')
- print(f'p-value: {p_value}')
- print(f'num lags: {n_lags}')
- print('Critial Values:')
- for key, value in critical_values.items():
- print(f' {key} : {value}')
- print(f'Result: The series is {"not " if p_value < 0.05 else ""}stationary')
-
-kpss_test(X1)
-kpss_test(X2)
+adf_test(data_df)
KPSS Statistic: 0.0016032868205162105
-p-value: 0.1
-num lags: 97
-Critial Values:
- 10% : 0.347
- 5% : 0.463
- 2.5% : 0.574
- 1% : 0.739
-Result: The series is stationary
-KPSS Statistic: 0.002692749007731491
-p-value: 0.1
-num lags: 97
-Critial Values:
- 10% : 0.347
- 5% : 0.463
- 2.5% : 0.574
- 1% : 0.739
-Result: The series is stationary
-
/opt/conda/lib/python3.8/site-packages/statsmodels/tsa/stattools.py:1850: FutureWarning: The behavior of using nlags=None will change in release 0.13.Currently nlags=None is the same as nlags="legacy", and so a sample-size lag length is used. After the next release, the default will change to be the same as nlags="auto" which uses an automatic lag length selection method. To silence this warning, either use "auto" or "legacy"
- warnings.warn(msg, FutureWarning)
-/opt/conda/lib/python3.8/site-packages/statsmodels/tsa/stattools.py:1885: InterpolationWarning: The test statistic is outside of the range of p-values available in the
-look-up table. The actual p-value is greater than the p-value returned.
+
+
+
+
+
+
+ p (mbar)
+ T (degC)
+
+
+
+
+ Test statistic
+ -38.6219
+ -41.3374
+
+
+ p-value
+ 0.0000
+ 0.0000
+
+
+ Critical value - 1%
+ -3.4304
+ -3.4304
+
+
+ Critical value - 5%
+ -2.8616
+ -2.8616
+
+
+ Critical value - 10%
+ -2.5668
+ -2.5668
+
+
+
+
Results: ADF Null Hypothesis is rejected. Thus, data is stationary. KPSS Null Hypothesis could not be rejected. Thus, data is stationary.
+Result: All three conclusively agree that both data are now stationary.
+We next split the data and select the lag order \(p\).
f2, (ax4, ax5) = plt.subplots(1, 2, figsize=(15, 5))
-f2.tight_layout()
-
-lag_plot(jena_sample['p (mbar)'], ax=ax4)
-ax4.set_title('p (mbar)');
-
-lag_plot(jena_sample['T (degC)'], ax=ax5)
-ax5.set_title('T (degC)');
-
-plt.show()
+train_df, test_df = splitter(data_df)
+
+
+
select_p(train_df)
AIC 59
+BIC 53
+HQIC 54
+FPE 59
+dtype: int64
+
Result: Lag plots confirm results of ADF test and KPSS test.
-Step 2: Set up a VAR model for the data (without differencing).
+We select \(p=30\). We finally fit our VAR model and test for Granger Causality.
model = VAR(train)
-model_fitted = model.fit(2)
-
/opt/conda/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
- warnings.warn('A date index has been provided, but it has no'
-/opt/conda/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:585: ValueWarning: A date index has been provided, but it is not monotonic and so will be ignored when e.g. forecasting.
- warnings.warn('A date index has been provided, but it is not'
-
Step 4: Make sure that the VAR is well-specified. For example, ensure that there is no serial correlation in the residuals. If need be, increase p until any autocorrelation issues are resolved.
-#Check for Serial Correlation of Residuals (Errors) using Durbin Watson Statistic
-#The value of this statistic can vary between 0 and 4.
-#The closer it is to the value 2, then there is no significant serial correlation.
-#The closer to 0, there is a positive serial correlation,
-#and the closer it is to 4 implies negative serial correlation.
-
-out = durbin_watson(model_fitted.resid)
-
-for col, val in zip(data.columns, out):
- print(col, ':', round(val, 2))
-
Rain : 2.01
-Dam : 2.0
-
Result: There is no significant correlation between in the residuals.
-Step 5: Now take the preferred VAR model and add in m additional lags of each of the variables into each of the equations.
-model = VAR(train)
-model_fitted = model.fit(2)
-#get the lag order
-lag_order = model_fitted.k_ar
-print(lag_order)
-
/opt/conda/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:581: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.
- warnings.warn('A date index has been provided, but it has no'
-/opt/conda/lib/python3.8/site-packages/statsmodels/tsa/base/tsa_model.py:585: ValueWarning: A date index has been provided, but it is not monotonic and so will be ignored when e.g. forecasting.
- warnings.warn('A date index has been provided, but it is not'
-
2
-
Step 6: Test for Granger non-causality.
-maxlag = lag_order
-test = 'ssr_chi2test'
-def grangers_causation_matrix(data, variables, test='ssr_chi2test', verbose=False):
- """Check Granger Causality of all possible combinations of the time series.
- The rows are the response variable, columns are predictors. The values in the table
- are the P-Values. P-Values lesser than the significance level (0.05), implies
- the Null Hypothesis that the coefficients of the corresponding past values is
- zero, that is, the X does not cause Y can be rejected.
-
- data : pandas dataframe containing the time series variables
- variables : list containing names of the time series variables.
- """
- df = pd.DataFrame(np.zeros((len(variables), len(variables))), columns=variables, index=variables)
- for c in df.columns:
- for r in df.index:
- test_result = grangercausalitytests(data[[r, c]], maxlag=maxlag, verbose=False)
- p_values = [round(test_result[i+1][0][test][1],4) for i in range(maxlag)]
- if verbose: print(f'Y = {r}, X = {c}, P Values = {p_values}')
- min_p_value = np.min(p_values)
- df.loc[r, c] = min_p_value
- df.columns = [var + '_x' for var in variables]
- df.index = [var + '_y' for var in variables]
- return df
-
-o = grangers_causation_matrix(train, variables = train.columns)
+p = 30
+model = VAR(train_df)
+var_model = model.fit(p)
o
+granger_causation_matrix(train_df, train_df.columns, p)
We observe that p “causes” T, but not the other way around.
-Causality will be revisited in a later chapter, in particular addressing the limitations of the method discussed in this chapter.
+Recall: If a given p-value is < significance level (0.05), then, the corresponding X series (column) causes the Y (row).
+Result: For this particular example, we can say that changes in pressure Granger causes changes in temperature. Conversely, changes in temperature also Granger causes pressure. This is another example of feedback. This means that pressure data improves changes in temperature prediction performance, and temperature data also improves pressure prediction performance.
+We have introduced the notion of causality in this chapter, and discussed its implications on time series analysis. We also applied the Granger Causality Test for linear VAR models for several datasets, seeing different examples of causality between the variables explored.
+Causality will be revisited in a later chapter, in particular addressing the limitations of the method discussed in this chapter and discussing causality for nonlinear models.
Given a chaotic time series, the following sets of images visualize how Empirical Dynamic Modelling tries to predict future values using the whole dataset rather that creating a parametrized equation. Let’s look at the following walkthrough. [Petchey, O. 2020]
Given the Time Series below, let’s try to predict the possible value or location of the pink dot (the succeeding dot in the time series) in the image below.
- +Since this is an empirical way of looking at data, (no-prior domain knowledge models, no parametrized equations), we will look at the prior dynamics that happened just before the pink dot (the few data points highlighted by the red lines)
- +Given that short history of the dynamics, we will look at the “past library” of dynamics using the whole dataset and pick those that look similar to the current dynamics that we have (the most similar ones highlighted by the blue lines)
- +The succeeding point of the selected prior dynamics with similar pattern or trajectory (blue lines) will have their next point in sequence (highlighted by the green dots)
- +This green dots will then produce valuable information that the system can infer where the next value in the whole sequence (pink dot) might be be located. One way of doing this is to project the values or the location of the green dots towards the front of the sequence. The correct location is Pink dot, Green dot denotes mean location of past values)
- +Using a time-shifted representation of the system above, using the lagged values corresponding to the number of points used as history, the red line would represent the latest movement of the dynamics and the blue lines would correspond to the most similar ones that can give valuable information for the prediction.
-Now let’s define a specific chaotic system that we can use as an example in the succeeding discussions.
@@ -505,12 +506,12 @@ The Lorenz system is notable for having chaotic solutions for certain parameter values and initial conditions. (“Butterfly Effect”). The term “Butterfly Effect” both signifies the characteristic of the Lorenz system of having possibly huge divergent values even with very small perturbations (“the flaps of a butterfly caused a tornado in the other side of the planet”) and the visual look of the system which looks like butterfly wings at certain angles.It’s a coupled dynamic system consisting of 3 differential equations (think of the axes as variables in a dynamic system). In an ecological examples, it could be a Resource-Prey-Predator dynamic system.
-# Visualize Lorenz Attractor [Piziniacco. L, 2020]
@@ -571,9 +572,10 @@ In an ecological examples, it could be a Resource-Prey-Predator dynamic system.<
In the visualization above, we see the that dynamic system (Lorenz) was plotted using the each of the point (or system states) computed from the differential equations. From here, we can define system states as points in a high-dimensional system.
Conversely, given a graph of a dynamic system, we can also extract the individual components or states of the system by projecting the dynamic system into on the axes. The axes can be thought as the fundamental state variables in a dynamic system. In an ecosystem, for example, these variables can correspond to population abundances, resources, or environmental conditions.
As an illustration, we can “extract” the values of the time series in one of the states (the Z-component for example) in the Lorenz Attractor above by projecting the 3D plot into just the Z-axis (which would just be similar to the z_out component in the code. Although time-series can represent independent state variables, in general, each time series is an observation function of the system state that can convolve several different state variables.
-
+
We can also extend the same concept to other state variables by projecting the high-dimensional graph into its individual axes.
-
the Lyanpunov exponents
There is also a 1-to-1 mapping betweent the original manifold and the shadow manifold. These enables us to reconstruct some of the properties of the original manifold by only using a lagged-time series of one of the axes/state variables
-mean absolute error (MAE) between the observation
forecast results (i.e., comparing \(Y(\mathbf{t_k} + 1)\) with \(\hat{Y}(\mathbf{t_k} +1)) \)
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+Requirement already satisfied: cycler>=0.10 in /Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages (from matplotlib>=2.2->pyEDM) (0.10.0)
+
Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.3 in /Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages (from matplotlib>=2.2->pyEDM) (2.4.7)
+Requirement already satisfied: kiwisolver>=1.0.1 in /Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages (from matplotlib>=2.2->pyEDM) (1.3.1)
+Requirement already satisfied: numpy>=1.15 in /Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages (from matplotlib>=2.2->pyEDM) (1.20.0)
+Requirement already satisfied: pillow>=6.2.0 in /Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages (from matplotlib>=2.2->pyEDM) (8.1.0)
Requirement already satisfied: six in /Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages (from cycler>=0.10->matplotlib>=2.2->pyEDM) (1.15.0)
Requirement already satisfied: pytz>=2017.3 in /Users/prince.javier/opt/anaconda3/envs/atsa/lib/python3.7/site-packages (from pandas>=0.20.3->pyEDM) (2021.1)
TentMap generated from the following function:
-First difference was taken: \(\mathbf{\triangle_t} = \mathbf{x_\mathbf{(t+1)}}- \mathbf{x_t} \)
Sample visualization of a tentmap is shown below: [11]
-# generate TentMap timeseries
@@ -800,27 +807,27 @@ Requirement already satisfied: pytz>=2017.3 in /Users/prince.javier/opt/anaco
0
0
- 0.436724
+ -0.317929
1
1
- -0.621780
+ 0.454183
2
2
- 0.251853
+ -0.726555
3
3
- 0.487632
+ 0.182084
4
4
- -0.974777
+ 0.363986
@@ -858,11 +865,11 @@ Requirement already satisfied: pytz>=2017.3 in /Users/prince.javier/opt/anaco
ADF Statistic: -12.471919
+ADF Statistic: -11.825553
p-value: 0.000000
Critical Values:
1%: -3.437
- 5%: -2.864
+ 5%: -2.865
10%: -2.568
@@ -1078,16 +1085,16 @@ Important properties of many natural systems is that nearby trajectories eventua
E rho
-0 1.0 0.749869
-1 2.0 0.994908
-2 3.0 0.987766
-3 4.0 0.972111
-4 5.0 0.925278
-5 6.0 0.804946
-6 7.0 0.713870
-7 8.0 0.653457
-8 9.0 0.578866
-9 10.0 0.534057
+0 1.0 0.812343
+1 2.0 0.996088
+2 3.0 0.980800
+3 4.0 0.947798
+4 5.0 0.863612
+5 6.0 0.766514
+6 7.0 0.579716
+7 8.0 0.504249
+8 9.0 0.475404
+9 10.0 0.402229
@@ -1174,16 +1181,16 @@ In the plot below, using Optimal Embedding E=2, we can plot the decreasing predi
E rho
-0 1.0 -0.017961
-1 2.0 -0.002996
-2 3.0 0.000203
-3 4.0 0.055508
-4 5.0 0.092762
-5 6.0 0.088180
-6 7.0 0.043276
-7 8.0 0.067235
-8 9.0 0.009978
-9 10.0 0.004450
+0 1.0 -0.013664
+1 2.0 -0.035236
+2 3.0 0.013915
+3 4.0 0.007673
+4 5.0 0.040837
+5 6.0 -0.020455
+6 7.0 -0.012874
+7 8.0 0.003359
+8 9.0 0.020575
+9 10.0 0.033107
@@ -1225,7 +1232,8 @@ comparing the performance of equivalent linear
(h = 0) and nonlinear (h > 0) S-map models, one can
distinguish nonlinear dynamical systems from linear
stochastic systems.
-
+
+
Compare S-Map Performance of a Logistic Map (Chaotic) and Gaussian Red Noise¶
In the steps below, we will try to distinguish differences between Chaotic Signals and Gaussian Red Noise, which may look similar visually.
@@ -1251,7 +1259,7 @@ stochastic systems.
-<matplotlib.legend.Legend at 0x7fc3db6295d0>
+<matplotlib.legend.Legend at 0x7fc6e7191590>
@@ -1731,7 +1739,7 @@ sufficient
top k = \(\sqrt(19)\), ~ top-4 or top-5 views based on forecasting skill
-
+
diff --git a/_build/html/06_ConvergentCrossMappingandSugiharaCausality/ccm_sugihara.html b/_build/html/06_ConvergentCrossMappingandSugiharaCausality/ccm_sugihara.html
index 7ec3184..9bd5c01 100644
--- a/_build/html/06_ConvergentCrossMappingandSugiharaCausality/ccm_sugihara.html
+++ b/_build/html/06_ConvergentCrossMappingandSugiharaCausality/ccm_sugihara.html
@@ -521,20 +521,20 @@
Attractors¶
-
+
An attractor is a “space” of states that the system tends to get attracted to as time goes on. When attractors can be thought of as curved spaces, they are called “manifolds.” I like to think of attractors as a way to summarize our system, like an embedding layer in a neural network architecture.
Q: What do you think is the simplest type of attractor?
Takens’ Embedding Theorem and Shadow Manifolds¶
-
+
Uzal, Lucas & Grinblat, G & Verdes, Pablo. (2011). Optimal reconstruction of dynamical systems: A noise amplification approach. Physical review. E, Statistical, nonlinear, and soft matter physics. 84. 016223. 10.1103/PhysRevE.84.016223.
From the term “shadow”, shadow manifolds are “projections” of the true system manifold on some variable \(X\). What Takens’ theorem tells us is if \(X\) belongs to a system \(S\) then we can generate a shadow manifold of the true manifold \(M_s\) using vectors of lagged (historical) values of \(X\). The points in this shadow manifold \(M_x\) will have a 1:1 correspondence with the points in the true (unknown) manifold \(M_s\).
Overview of CCM¶
-
+
Tsonis A.A., Deyle E.R., Ye H., Sugihara G. (2018) Convergent Cross Mapping: Theory and an Example. In: Tsonis A. (eds) Advances in Nonlinear Geosciences. Springer, Cham. https://doi.org/10.1007/978-3-319-58895-7_27
Cross Mapping¶
@@ -622,7 +622,7 @@
-<matplotlib.legend.Legend at 0x7f9567a14e90>
+<matplotlib.legend.Legend at 0x7f8ad660ec10>
@@ -644,7 +644,7 @@
-(0.005395539983091767, 0.8646878689811068)
+(0.005395539983091772, 0.8646878689811068)
@@ -1075,7 +1075,7 @@ def plot_ccm_correls(self):
-<matplotlib.legend.Legend at 0x7f9552ac0bd0>
+<matplotlib.legend.Legend at 0x7f8ac124b4d0>
@@ -1210,7 +1210,7 @@ def plot_ccm_correls(self):
-<matplotlib.legend.Legend at 0x7f9552a2b950>
+<matplotlib.legend.Legend at 0x7f8ac12a0c10>
@@ -1233,7 +1233,7 @@ def plot_ccm_correls(self):
-(0.24813484131913205, 1.6963889777956713e-15)
+(0.24813484131913208, 1.6963889777954784e-15)
@@ -1806,7 +1806,7 @@ Y->X r 0.2 p value 0.0
Dam System Inferred Causal Relationships¶
Based on the results above, we can infer a network of causal relationships. Relationships with unclear convergence are shown in broken lines while relationships with clear convergence are shown in solid lines.
-
+
Jena climate data¶
@@ -2034,7 +2034,7 @@ Y->X r 0.69 p value 0.0
Inferred Climate System Causal Relationships¶
-
+
Based on the results above, we can infer a network of causal relationships. There seems to be a strong feedback loops between all three elements in the system. Upon checking past researches on the topic, we find that there are papers that support the seemingly unintuitive interactions in the inferred causal network:
Evolution of South Atlantic density and chemical stratification across the last deglaciation
diff --git a/_build/html/06_ConvergentCrossMappingandSugiharaCausality/using_causal_ccm_package.html b/_build/html/06_ConvergentCrossMappingandSugiharaCausality/using_causal_ccm_package.html
index 561aaf7..adfa35d 100644
--- a/_build/html/06_ConvergentCrossMappingandSugiharaCausality/using_causal_ccm_package.html
+++ b/_build/html/06_ConvergentCrossMappingandSugiharaCausality/using_causal_ccm_package.html
@@ -453,7 +453,7 @@
-(0.2775286246309841, 5.4283283439476714e-126)
+(0.27752862463098416, 5.428328343942734e-126)
@@ -505,7 +505,7 @@
Y->X r 0.02 p value 0.0775
-<matplotlib.legend.Legend at 0x7fad1e31db50>
+<matplotlib.legend.Legend at 0x7fd2ae393690>
diff --git a/_build/html/07_CrosscorrelationsFourierTransformandWaveletTransform/07_CrosscorrelationsFourierTransformandWaveletTransform.html b/_build/html/07_CrosscorrelationsFourierTransformandWaveletTransform/07_CrosscorrelationsFourierTransformandWaveletTransform.html
index ebfd6c1..03e84d6 100644
--- a/_build/html/07_CrosscorrelationsFourierTransformandWaveletTransform/07_CrosscorrelationsFourierTransformandWaveletTransform.html
+++ b/_build/html/07_CrosscorrelationsFourierTransformandWaveletTransform/07_CrosscorrelationsFourierTransformandWaveletTransform.html
@@ -505,7 +505,7 @@
-Maximum at: 0.236 (in $s$)
+Maximum at: 0.25 (in $s$)
@@ -859,8 +859,8 @@ Critical Values:
The Fourier Transform:¶
Transforming a signal from the time domain into the frequency (\(\omega\)) domain using this method is called the \textbf{Fourier Transform (FT)}. The FT is given by:
-
-(12)¶\[\begin{align} \hat{y}(\omega) = \int_{-\infty}^{\infty}{y(t)e^{-2\pi i \omega t}d\omega} \end{align}\]
+
+(12)¶\[\begin{align} \hat{y}(\omega) = \int_{-\infty}^{\infty}{y(t)e^{-2\pi i \omega t}d\omega} \end{align}\]
To better understand the FT, let us take a look at some of its applications.
FT of a Pure Signal¶
@@ -974,8 +974,8 @@ Critical Values:
Noise Filtering¶
Real time series data are never free from noise making it tricky to find the real dynamics of whatever it is measuring. We may end up trying to model noise and end up overlooking the real behavior of the time series.
Thankfully, we can manipulate time series data in the frequency domain to eliminate one of the most types of noise - white noise. White noise pervades time series data and by definition, has components across all frequencies. Usually, a time series with white noise is represented as:
-
-(13)¶\[\begin{align} y(t) = s(t) + v(t) \end{align}\]
+
+(13)¶\[\begin{align} y(t) = s(t) + v(t) \end{align}\]
where \(s(t)\) is the true signal we want to retrieve from \(y(t)\) and \(v(t)\) is white noise we want to eliminate. We simulate this below by adding white noise to the signal.
Filtering by Energy Level¶
@@ -1040,41 +1040,42 @@ Critical Values:
-Peaks at: [ 0.4 1.4 2. 2.6 3.2 4.2 4.8 6.4 7. 7.4 8. 8.6
- 9.2 9.8 10.4 10.8 11.8 12.2 12.8 13.6 14. 15. 15.6 16.2
- 17. 18. 18.4 19.2 19.6 20.2 21. 21.6 22.2 22.6 23.2 23.8
- 24.6 25.2 25.6 26.4 26.8 27.4 28. 28.8 29.4 30.4 30.8 31.2
- 31.6 32.4 33.2 33.6 34.2 34.6 35.2 35.8 36.6 37.6 38.2 38.8
- 39.4 40.2 41. 41.4 42.2 43. 43.8 44.2 44.6 45.2 45.8 46.4
- 46.8 47.4 48.2 48.8 49.6 50.8 51.2 52.2 53. 53.4 53.8 54.4
- 55.2 55.6 56. 56.4 56.8 57.4 57.8 58.4 59.4 59.8 60.4 61.
- 61.6 62. 62.6 63.2 64. 64.6 65.2 65.8 66.4 67. 67.8 69.
- 69.6 70. 71.4 71.8 72.8 73.2 73.6 74. 75.2 75.8 76.6 77.
- 77.8 78.6 79. 79.8 80.6 81.2 81.6 82.4 82.8 83.2 83.6 84.8
- 85.2 85.6 86. 86.6 87.2 87.6 88.2 88.8 89.2 90. 90.6 91.2
- 91.6 92.2 92.8 93.4 94. 94.8 95.6 96. 96.6 97.2 97.6 98.
- 98.6 99. 99.8 100.2 101.2 102. 102.8 103.2 103.8 104.2 104.6 105.
- 105.6 106. 106.4 107. 107.6 108. 108.8 109.4 110. 111.2 112.2 112.8
- 113.6 114.2 114.6 115.6 116.2 116.6 117. 117.4 118. 118.6 119.2 120.
- 120.4 121.4 121.8 122.4 123. 123.8 124.4 124.8 125.4 126.2 126.8 127.4
- 128.4 129. 129.4 129.8 130.4 131. 132. 132.4 133.2 133.8 134.2 134.8
- 135.2 136. 136.4 137. 137.6 138. 138.6 139.2 139.6 140.2 140.6 141.6
- 142. 142.4 143.8 144.6 145.4 146. 146.8 147.2 148. 148.4 148.8 149.4
- 149.8 150.4 150.8 151.4 152.2 153. 153.4 153.8 154.4 155. 155.4 156.
- 156.6 157.2 158. 158.4 159. 159.8 160.2 161. 161.4 162.2 163. 163.4
- 164. 164.6 165. 165.8 166.2 167. 167.6 168. 168.4 168.8 169.2 169.6
- 170. 170.4 171. 172. 172.6 173. 174.2 174.6 175. 175.4 176.2 176.6
- 177.2 177.8 178.2 178.8 179.6 180. 180.4 181.4 182. 182.8 183.2 183.6
- 184.4 185. 185.4 186. 186.8 187.2 187.6 188.4 189.2 189.6 190.2 190.8
- 191.2 192. 192.4 192.8 193.6 194. 194.8 195.4 196.2 196.8 197.8 198.4
- 199. 199.4 200.4 200.8 201.2 201.8 202.4 203. 203.6 204. 204.8 205.2
- 205.6 206.2 206.8 207.6 208.4 208.8 209.4 210. 210.6 211.6 212. 212.4
- 212.8 213.6 214. 214.6 215.2 216. 216.8 217.2 217.6 218.4 218.8 219.2
- 219.6 220.6 221.4 221.8 222.4 222.8 223.6 224.2 225.8 226.2 226.6 227.4
- 228. 228.4 228.8 229.4 230. 230.6 231. 231.6 232. 232.6 233. 234.
- 234.8 235.2 235.6 236.8 237.2 238.2 238.8 239.2 239.6 240.4 241.2 241.6
- 242.2 242.6 243.2 243.6 244. 244.6 245. 245.8 246.6 247. 247.6 248.
- 248.8 249.6]
+Peaks at: [ 0.8 1.2 1.6 2. 2.6 3.2 4. 4.6 5. 5.8 6.2 7.
+ 7.6 8.2 8.8 9.8 11. 11.6 12.6 13.6 14.2 15. 15.4 16.2
+ 17. 17.4 18.4 18.8 19.4 20. 20.6 21.4 21.8 22.6 23.2 23.6
+ 24. 24.6 25.2 26. 26.4 27.2 27.6 28. 28.4 29.2 29.6 30.4
+ 31.2 31.8 32.4 33.2 33.8 34.2 34.6 35. 35.4 36.2 36.8 37.6
+ 38.4 39.4 39.8 40.2 40.6 41. 41.4 41.8 42.2 42.6 43.4 44.
+ 44.4 44.8 45.8 46.6 47.4 48.2 48.6 49. 49.4 50. 51. 51.6
+ 52. 52.4 53.8 54.2 54.6 55.4 55.8 56.4 57. 57.6 58. 58.4
+ 59. 59.6 60.2 60.6 61.4 62. 63. 63.6 64.4 64.8 65.4 65.8
+ 66.2 66.6 67.2 67.8 68.4 69. 69.4 70.2 70.8 71.2 71.8 72.2
+ 72.8 73.4 73.8 74.8 75.4 76.4 77. 77.4 78. 78.4 79. 79.4
+ 79.8 80.2 80.6 81.4 82. 82.6 83.2 83.8 84.4 84.8 85.4 85.8
+ 86.4 87.4 87.8 88.6 89.4 90.2 91.2 91.6 92.2 93.2 93.8 94.2
+ 94.8 95.2 95.6 96.4 96.8 97.6 98. 98.8 99.6 100.2 100.8 101.6
+ 102. 102.4 103. 104. 104.6 105.2 106. 106.4 106.8 107.2 107.6 108.2
+ 109.4 110. 110.8 111.2 111.8 112.4 113. 113.8 114.2 114.8 115.2 115.6
+ 116.2 116.6 117. 117.8 118.4 118.8 119.4 120. 120.8 121.6 122.4 123.2
+ 124.4 125.2 126. 126.8 127.4 128. 128.6 129. 129.6 130.2 130.6 131.
+ 131.4 131.8 132.6 133.2 133.6 134.2 134.8 135.2 135.6 136. 136.6 137.2
+ 137.8 138.2 139. 140. 140.4 140.8 141.6 142.4 143.2 143.6 144. 144.4
+ 144.8 145.2 145.8 146.4 146.8 147.2 147.6 148.4 149.2 149.8 150.2 150.6
+ 151.4 151.8 152.4 153. 153.6 154.6 155. 155.8 156.4 156.8 157.4 158.
+ 158.6 159.2 159.8 160.6 161.4 161.8 162.2 162.6 163. 163.6 164.6 165.
+ 165.8 166.4 166.8 167.2 167.8 168.4 169.2 170.4 170.8 171.4 172.2 172.8
+ 174. 174.6 175.2 176. 176.4 176.8 177.4 178.2 178.8 179.2 179.8 180.2
+ 180.8 181.2 182. 182.6 183. 183.8 184.2 184.6 185. 185.6 186.2 186.8
+ 187.2 187.6 188.2 188.6 189.2 189.6 190.4 191. 191.6 192. 192.6 193.2
+ 193.6 194. 194.8 195.2 195.8 196.2 197. 197.4 198.2 198.6 199.6 200.
+ 200.4 200.8 201.2 201.8 202.2 202.6 203.2 203.8 204.2 205. 205.4 205.8
+ 206.6 207. 207.6 208. 208.6 209.2 209.6 210.2 210.6 211.2 212.2 212.8
+ 213.2 213.8 214.2 215. 215.6 216.2 216.8 217.6 218. 218.6 219.2 220.2
+ 221. 221.6 222. 222.4 222.8 223.4 223.8 224.2 224.8 225.4 226. 226.4
+ 227.2 227.8 228.4 229.2 229.6 230.2 230.8 231.4 231.8 232.4 233.2 233.6
+ 234.8 235.6 236.6 237.2 237.6 238.4 239. 239.6 240. 240.4 241. 241.6
+ 242.2 242.8 243.2 243.8 244.2 244.6 245.4 245.8 246.6 247.6 248.2 248.8
+ 249.4]
@@ -1092,7 +1093,7 @@ Critical Values:
-Peaks at: [ 17. 60.4 67. 224.2 246.8]
+Peaks at: [ 9.8 17. ]
@@ -1346,7 +1347,7 @@ Critical Values:
[<matplotlib.lines.Line2D at 0x7fe67a606350>]
+
[<matplotlib.lines.Line2D at 0x7f9976353550>]
[<matplotlib.lines.Line2D at 0x7fe67a89a810>]
+[<matplotlib.lines.Line2D at 0x7f9967cc3150>]
@@ -1381,7 +1382,7 @@ Critical Values:
[<matplotlib.lines.Line2D at 0x7fe67a9b7dd0>]
+[<matplotlib.lines.Line2D at 0x7f996800fd10>]
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diff --git a/_build/html/_sources/04_GrangerCausality/04_GrangerCausality.ipynb b/_build/html/_sources/04_GrangerCausality/04_GrangerCausality.ipynb
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--- a/_build/html/_sources/04_GrangerCausality/04_GrangerCausality.ipynb
+++ b/_build/html/_sources/04_GrangerCausality/04_GrangerCausality.ipynb
@@ -6,20 +6,14 @@
"source": [
"# Chapter 4: Granger Causality Test\n",
"\n",
- "In the first three chapters, we discussed the classical methods for both univariate and multivariate time series forecasting. We now introduce the notion of causality and its implications on time series analysis in general. We also describe a test for the linear VAR model discussed in the previous chapter.\n",
- "\n",
- "Prepared by: Carlo Vincienzo G. Dajac"
+ "In the first three chapters, we discussed the classical methods for both univariate and multivariate time series forecasting. We now introduce the notion of causality and its implications on time series analysis in general. We also describe a test for the linear VAR model discussed in the previous chapter."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "**Chapter Outline**\n",
- "* Notations\n",
- "* Definitions\n",
- "* Assunmptions\n",
- "* Testing for Granger Causality"
+ "Prepared by: Carlo Vincienzo G. Dajac"
]
},
{
@@ -32,7 +26,7 @@
"\n",
"Denote the optimum, unbiased, least-squares predictor of $A_t$ using the set of values $B_t$ by $P_t (A|B)$. Thus, for instance, $P_t (X|\\overline X)$ will be the optimum predictor of $X_t$ using only past $X_t$. The predictive error series will be denoted by $\\varepsilon_t(A|B) = A_t - P_t(A|B)$. Let $\\sigma^2 (A|B)$ be the variance of $\\varepsilon_t(A|B)$.\n",
"\n",
- "Let $U_t$ be all the information in the universe accumulated since time $t-1$ and let $U_t - Y_t$ denote all this information *apart* from the specified series $Y_t$."
+ "Let $U_t$ be all the information in the universe accumulated since time $t-1$ and let $U_t - Y_t$ denote all this information *apart* from the specified series $Y_t$, which is another stationary time series that is different from $X_t$."
]
},
{
@@ -41,10 +35,9 @@
"source": [
"## Definitions\n",
"\n",
- "\n",
"### Causality\n",
"\n",
- "If $\\sigma^2 (X|U) < \\sigma^2 (X| \\overline{U-Y})$, we say that $Y$ is causing $X$, denoted by $Y_t \\implies X_t$. We say that $Y_t$ is causing $X_t$ if we are able to predict $X_t$ using all available information than if the information apart from $Y_t$ had been used.\n",
+ "If $\\sigma^2 (X|U) < \\sigma^2 (X| \\overline{U-Y})$, we say that $Y$ is causing $X$, denoted by $Y_t \\implies X_t$. We say that $Y_t$ is causing $X_t$ if we are **able to predict** $X_t$ using all available information than if the information apart from $Y_t$ had been used.\n",
"\n",
"### Feedback\n",
"If $\\sigma^2 (X|\\overline U) < \\sigma^2 (X| \\overline{U-Y})$ and $\\sigma^2 (Y|\\overline U) < \\sigma^2 (Y| \\overline{U-X})$, we say that feedback is occurring, which is denoted by $Y_t \\iff X_t$, i.e., feedback is said to occur when $X_t$ is causing $Y_t$ and also $Y_t$ is causing $X_t$.\n",
@@ -62,56 +55,48 @@
"source": [
"## Assumptions\n",
"\n",
- "* Series is stationary.\n",
- "* Linear model is already optimized."
+ "* $X_t$ and $Y_t$ are stationary.\n",
+ "* $P_t (A|B)$ is already optimized."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Testing for Granger Causality"
+ "## Testing for Granger Causality\n",
+ "\n",
+ "We will be first building VAR models for our examples in this section. In addition to the steps outlined in the previous chapter, we will just call built-in Granger causality test function and configure it accordingly."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import pandas as pd\n",
+ "import numpy as np\n",
+ "import matplotlib.pyplot as plt\n",
+ "from pandas.plotting import lag_plot\n",
+ "from statsmodels.tsa.vector_ar.var_model import VAR\n",
+ "from statsmodels.tsa.stattools import adfuller, kpss, grangercausalitytests\n",
+ "import warnings\n",
+ "warnings.filterwarnings(\"ignore\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Example 1: Ipo Dam Dataset\n",
+ "\n",
+ "We will use the Ipo dataset in this example. It contains daily measurements of the following variables: rainfall (in millimeters), Oceanic Niño Index (ONI), NIA release flow (in cubic meters per second), and dam water level (in meters), respectively."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
- "outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "/Users/prince.javier/opt/anaconda3/lib/python3.7/site-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
- " import pandas.util.testing as tm\n"
- ]
- }
- ],
- "source": [
- "import pandas as pd\n",
- "import numpy as np\n",
- "import matplotlib.pyplot as plt\n",
- "from scipy import stats\n",
- "from pandas.plotting import lag_plot\n",
- "from statsmodels.tsa.api import VAR\n",
- "from statsmodels.tsa.stattools import adfuller\n",
- "from statsmodels.tsa.stattools import kpss\n",
- "from statsmodels.tsa.stattools import grangercausalitytests\n",
- "from statsmodels.tools.eval_measures import rmse, aic\n",
- "from statsmodels.stats.stattools import durbin_watson"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We will use the Ipo dataset in this notebook."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
"outputs": [
{
"data": {
@@ -150,125 +135,105 @@
" \n",
" \n",
" 0 \n",
- " 0.00 \n",
+ " 0.0 \n",
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" 38.225693 \n",
" 100.70 \n",
" \n",
" \n",
" 1 \n",
- " 0.00 \n",
+ " 0.0 \n",
" -0.7 \n",
" 57.996530 \n",
" 100.63 \n",
" \n",
" \n",
" 2 \n",
- " 0.00 \n",
+ " 0.0 \n",
" -0.7 \n",
" 49.119213 \n",
" 100.56 \n",
" \n",
" \n",
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" 100.55 \n",
" \n",
" \n",
" 4 \n",
- " 0.00 \n",
+ " 0.0 \n",
" -0.7 \n",
" 42.223380 \n",
" 100.48 \n",
" \n",
- " \n",
- " ... \n",
- " ... \n",
- " ... \n",
- " ... \n",
- " ... \n",
- " \n",
- " \n",
- " 7111 \n",
- " 1.80 \n",
- " -0.2 \n",
- " 5.040000 \n",
- " 100.86 \n",
- " \n",
- " \n",
- " 7112 \n",
- " 1.60 \n",
- " -0.2 \n",
- " 4.500000 \n",
- " 101.01 \n",
- " \n",
- " \n",
- " 7113 \n",
- " 21.60 \n",
- " -0.2 \n",
- " 6.730000 \n",
- " 101.08 \n",
- " \n",
- " \n",
- " 7114 \n",
- " 0.20 \n",
- " -0.2 \n",
- " 6.720000 \n",
- " 100.92 \n",
- " \n",
- " \n",
- " 7115 \n",
- " 46.82 \n",
- " -0.2 \n",
- " 1.950000 \n",
- " 100.97 \n",
- " \n",
" \n",
"\n",
- "7116 rows × 4 columns
\n",
"
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.018 | \n", + "1.8045 | \n", + "
p-value | \n", + "0.100 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.6223 | \n", + "-5.8742 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0179 | \n", + "0.0047 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.6227 | \n", + "-21.5919 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "38.225693 | \n", + "100.70 | \n", + "
1 | \n", + "57.996530 | \n", + "100.63 | \n", + "
2 | \n", + "49.119213 | \n", + "100.56 | \n", + "
3 | \n", + "47.034720 | \n", + "100.55 | \n", + "
4 | \n", + "42.223380 | \n", + "100.48 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.184 | \n", + "1.8045 | \n", + "
p-value | \n", + "0.022 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-6.6030 | \n", + "-5.8742 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0048 | \n", + "0.0047 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-21.2837 | \n", + "-21.5919 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA_x | \n", + "Dam_x | \n", + "
---|---|---|
NIA_y | \n", + "1.0000 | \n", + "0.0007 | \n", + "
Dam_y | \n", + "0.0216 | \n", + "1.0000 | \n", + "
\n", + " | Rain | \n", + "ONI | \n", + "NIA | \n", + "Dam | \n", + "
---|---|---|---|---|
Time | \n", + "\n", + " | \n", + " | \n", + " | \n", + " |
0 | \n", + "0.0 | \n", + "-0.7 | \n", + "38.225693 | \n", + "78.63 | \n", + "
1 | \n", + "0.0 | \n", + "-0.7 | \n", + "57.996530 | \n", + "78.63 | \n", + "
2 | \n", + "0.0 | \n", + "-0.7 | \n", + "49.119213 | \n", + "78.61 | \n", + "
3 | \n", + "0.0 | \n", + "-0.7 | \n", + "47.034720 | \n", + "78.59 | \n", + "
4 | \n", + "0.0 | \n", + "-0.7 | \n", + "42.223380 | \n", + "78.56 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "0.0 | \n", + "78.63 | \n", + "
1 | \n", + "0.0 | \n", + "78.63 | \n", + "
2 | \n", + "0.0 | \n", + "78.61 | \n", + "
3 | \n", + "0.0 | \n", + "78.59 | \n", + "
4 | \n", + "0.0 | \n", + "78.56 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0327 | \n", + "1.8845 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.7136 | \n", + "-4.2004 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0007 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0327 | \n", + "0.0226 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.7138 | \n", + "-26.5948 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain_x | \n", + "Dam_x | \n", + "
---|---|---|
Rain_y | \n", + "1.0 | \n", + "0.0005 | \n", + "
Dam_y | \n", + "0.0 | \n", + "1.0000 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "38.225693 | \n", + "78.63 | \n", + "
1 | \n", + "57.996530 | \n", + "78.63 | \n", + "
2 | \n", + "49.119213 | \n", + "78.61 | \n", + "
3 | \n", + "47.034720 | \n", + "78.59 | \n", + "
4 | \n", + "42.223380 | \n", + "78.56 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.184 | \n", + "1.8845 | \n", + "
p-value | \n", + "0.022 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-6.6030 | \n", + "-4.2004 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0007 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0048 | \n", + "0.0226 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-21.2837 | \n", + "-26.5948 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "0.2295 | \n", + "0.3649 | \n", + "
p-value | \n", + "0.0100 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "-18.3281 | \n", + "-8.5824 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4304 | \n", + "-3.4304 | \n", + "
Critical value - 5% | \n", + "-2.8616 | \n", + "-2.8616 | \n", + "
Critical value - 10% | \n", + "-2.5668 | \n", + "-2.5668 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "0.0009 | \n", + "0.0024 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "-38.6219 | \n", + "-41.3374 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4304 | \n", + "-3.4304 | \n", + "
Critical value - 5% | \n", + "-2.8616 | \n", + "-2.8616 | \n", + "
Critical value - 10% | \n", + "-2.5668 | \n", + "-2.5668 | \n", + "
\n", - " | p (mbar) | \n", - "T (degC) | \n", - "Tpot (K) | \n", - "Tdew (degC) | \n", - "rh (%) | \n", - "VPmax (mbar) | \n", - "VPact (mbar) | \n", - "VPdef (mbar) | \n", - "sh (g/kg) | \n", - "H2OC (mmol/mol) | \n", - "rho (g/m**3) | \n", - "wv (m/s) | \n", - "max. wv (m/s) | \n", - "wd (deg) | \n", - "
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Date Time | \n", - "\n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " | \n", - " |
2009-01-01 00:10:00 | \n", - "996.52 | \n", - "-8.02 | \n", - "265.40 | \n", - "-8.90 | \n", - "93.3 | \n", - "3.33 | \n", - "3.11 | \n", - "0.22 | \n", - "1.94 | \n", - "3.12 | \n", - "1307.75 | \n", - "1.03 | \n", - "1.75 | \n", - "152.3 | \n", - "
2009-01-01 00:20:00 | \n", - "996.57 | \n", - "-8.41 | \n", - "265.01 | \n", - "-9.28 | \n", - "93.4 | \n", - "3.23 | \n", - "3.02 | \n", - "0.21 | \n", - "1.89 | \n", - "3.03 | \n", - "1309.80 | \n", - "0.72 | \n", - "1.50 | \n", - "136.1 | \n", - "
2009-01-01 00:30:00 | \n", - "996.53 | \n", - "-8.51 | \n", - "264.91 | \n", - "-9.31 | \n", - "93.9 | \n", - "3.21 | \n", - "3.01 | \n", - "0.20 | \n", - "1.88 | \n", - "3.02 | \n", - "1310.24 | \n", - "0.19 | \n", - "0.63 | \n", - "171.6 | \n", - "
7116 rows × 4 columns
\n", "\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.018 | \n", + "1.8045 | \n", + "
p-value | \n", + "0.100 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.6223 | \n", + "-5.8742 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0179 | \n", + "0.0047 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.6227 | \n", + "-21.5919 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "38.225693 | \n", + "100.70 | \n", + "
1 | \n", + "57.996530 | \n", + "100.63 | \n", + "
2 | \n", + "49.119213 | \n", + "100.56 | \n", + "
3 | \n", + "47.034720 | \n", + "100.55 | \n", + "
4 | \n", + "42.223380 | \n", + "100.48 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.184 | \n", + "1.8045 | \n", + "
p-value | \n", + "0.022 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-6.6030 | \n", + "-5.8742 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0048 | \n", + "0.0047 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-21.2837 | \n", + "-21.5919 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA_x | \n", + "Dam_x | \n", + "
---|---|---|
NIA_y | \n", + "1.0000 | \n", + "0.0007 | \n", + "
Dam_y | \n", + "0.0216 | \n", + "1.0000 | \n", + "
\n", + " | Rain | \n", + "ONI | \n", + "NIA | \n", + "Dam | \n", + "
---|---|---|---|---|
Time | \n", + "\n", + " | \n", + " | \n", + " | \n", + " |
0 | \n", + "0.0 | \n", + "-0.7 | \n", + "38.225693 | \n", + "78.63 | \n", + "
1 | \n", + "0.0 | \n", + "-0.7 | \n", + "57.996530 | \n", + "78.63 | \n", + "
2 | \n", + "0.0 | \n", + "-0.7 | \n", + "49.119213 | \n", + "78.61 | \n", + "
3 | \n", + "0.0 | \n", + "-0.7 | \n", + "47.034720 | \n", + "78.59 | \n", + "
4 | \n", + "0.0 | \n", + "-0.7 | \n", + "42.223380 | \n", + "78.56 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "0.0 | \n", + "78.63 | \n", + "
1 | \n", + "0.0 | \n", + "78.63 | \n", + "
2 | \n", + "0.0 | \n", + "78.61 | \n", + "
3 | \n", + "0.0 | \n", + "78.59 | \n", + "
4 | \n", + "0.0 | \n", + "78.56 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0327 | \n", + "1.8845 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.7136 | \n", + "-4.2004 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0007 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0327 | \n", + "0.0226 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | Rain | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-8.7138 | \n", + "-26.5948 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | Rain_x | \n", + "Dam_x | \n", + "
---|---|---|
Rain_y | \n", + "1.0 | \n", + "0.0005 | \n", + "
Dam_y | \n", + "0.0 | \n", + "1.0000 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Time | \n", + "\n", + " | \n", + " |
0 | \n", + "38.225693 | \n", + "78.63 | \n", + "
1 | \n", + "57.996530 | \n", + "78.63 | \n", + "
2 | \n", + "49.119213 | \n", + "78.61 | \n", + "
3 | \n", + "47.034720 | \n", + "78.59 | \n", + "
4 | \n", + "42.223380 | \n", + "78.56 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.184 | \n", + "1.8845 | \n", + "
p-value | \n", + "0.022 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.216 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.176 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.146 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.119 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-6.6030 | \n", + "-4.2004 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0007 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "0.0048 | \n", + "0.0226 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | NIA | \n", + "Dam | \n", + "
---|---|---|
Test statistic | \n", + "-21.2837 | \n", + "-26.5948 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4313 | \n", + "-3.4313 | \n", + "
Critical value - 5% | \n", + "-2.8619 | \n", + "-2.8619 | \n", + "
Critical value - 10% | \n", + "-2.5670 | \n", + "-2.5670 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "0.2295 | \n", + "0.3649 | \n", + "
p-value | \n", + "0.0100 | \n", + "0.0100 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "-18.3281 | \n", + "-8.5824 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4304 | \n", + "-3.4304 | \n", + "
Critical value - 5% | \n", + "-2.8616 | \n", + "-2.8616 | \n", + "
Critical value - 10% | \n", + "-2.5668 | \n", + "-2.5668 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "0.0009 | \n", + "0.0024 | \n", + "
p-value | \n", + "0.1000 | \n", + "0.1000 | \n", + "
Critical value - 1% | \n", + "0.2160 | \n", + "0.2160 | \n", + "
Critical value - 2.5% | \n", + "0.1760 | \n", + "0.1760 | \n", + "
Critical value - 5% | \n", + "0.1460 | \n", + "0.1460 | \n", + "
Critical value - 10% | \n", + "0.1190 | \n", + "0.1190 | \n", + "
\n", + " | p (mbar) | \n", + "T (degC) | \n", + "
---|---|---|
Test statistic | \n", + "-38.6219 | \n", + "-41.3374 | \n", + "
p-value | \n", + "0.0000 | \n", + "0.0000 | \n", + "
Critical value - 1% | \n", + "-3.4304 | \n", + "-3.4304 | \n", + "
Critical value - 5% | \n", + "-2.8616 | \n", + "-2.8616 | \n", + "
Critical value - 10% | \n", + "-2.5668 | \n", + "-2.5668 | \n", + "