From 04596cab4db4df49903670d52a168f131ed64472 Mon Sep 17 00:00:00 2001 From: Prince Joseph Javier Date: Tue, 23 Feb 2021 00:15:16 +0800 Subject: [PATCH] updated intro --- 00_Introduction/00_Introduction.ipynb | 4 +- .../00_Introduction/00_Introduction.doctree | Bin 471637 -> 496877 bytes _build/.doctrees/environment.pickle | Bin 171640 -> 174664 bytes .../html/00_Introduction/00_Introduction.html | 92 ++++++++++++- _build/html/_images/00_Introduction_10_0.png | Bin 40900 -> 42765 bytes _build/html/_images/00_Introduction_12_0.png | Bin 24952 -> 24473 bytes _build/html/_images/00_Introduction_14_0.png | Bin 56576 -> 58985 bytes _build/html/_images/00_Introduction_16_0.png | Bin 54636 -> 56325 bytes _build/html/_images/00_Introduction_20_0.png | Bin 6602 -> 7258 bytes _build/html/_images/00_Introduction_20_1.png | Bin 6602 -> 7258 bytes _build/html/_images/00_Introduction_21_0.png | Bin 6602 -> 7258 bytes _build/html/_images/00_Introduction_21_1.png | Bin 6602 -> 7258 bytes 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  • + + 4. Benchmark Methods + + +
  • - 3. Evaluation Metrics for Forecast Accuracy + 5. Evaluation Metrics for Forecast Accuracy
  • +
  • + + 6. Summary of Forecast Accuracy for Jena Climate Dataset + +
  • @@ -381,6 +403,8 @@ import matplotlib.pyplot as plt import statsmodels.graphics.tsaplots as tg %matplotlib inline + +plt.rcParams['figure.figsize'] = [15, 2] @@ -709,8 +733,31 @@

    with the characteristic polynomials as defined above.

    +
    +

    4. Benchmark Methods¶

    +

    In order to properly measure the performance of a forecasting model, we first need to establish several baselines. This section introduces several methods that will serve as benchmarks. Obviously, any forecasting method we develop must beat these benchmarks. Otherwise, the new method is not even worth considering.

    +

    In the notation below, \(T\) refers to the length of the time series and \(h\) refers to the prediction horizon.

    +
    +

    Naïve Method¶

    +

    Forecasts of all future values are equal to the last observation.

    +
    +\[\begin{align*} + \hat{y}_{T+h} &= y_T +\end{align*}\]
    +
    +
    +

    Seasonal Naïve Method¶

    +

    Forecasts are equal to the last observed value from the same season of the year (e.g. the same month of the previous year).

    +
    +\[\begin{align*} + \hat{y}_{T+h} &= y_{T+h-m(k+1)} +\end{align*}\]
    +

    where \(m\) is the seasonal period and \(k\) is the integer part of \((h-1)/m\) (i.e. the number of complete years in the forecast period prior to time \(T+h\)).

    +

    As an example, if we were forecasting a monthly time series, the forecast for all future February values is simply equal to the last observed February value. With weekly data, the forecast of all future Friday values is equal to the last observed Friday value. And so on.

    +
    +
    -

    3. Evaluation Metrics for Forecast Accuracy¶

    +

    5. Evaluation Metrics for Forecast Accuracy¶

    Forecasting is one of the most common inference tasks in time series analysis. In order to properly gauge the performance of a time series model, it is common practice to divide the dataset into two parts: training and test data. Model parameters are estimated using training data, then the models are used to generate forecasts that are evaluated against the test data.

    Error statistics come in different flavors, each with their own advantages and disadvantages.

    @@ -746,6 +793,47 @@ \end{align*}\]
    +
    +

    6. Summary of Forecast Accuracy for Jena Climate Dataset¶

    +

    The handbook goes over several time series forecasting methods and compares performance of said models on the Jena Climate Dataset. Specifically, each method attempts to forecast the temperature variable (in Celsius). A summary of the forecast accuracy for each model is shown below.

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    MethodAverage MAE (Celsius)
    Naive3.18
    Seasonal Naive2.61
    Linear Regression2.86
    ARIMA3.19
    VAR2.54
    Simplex Method (pending validation)1.53
    LightGBM2.08