.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/LinearModels/SARIMA.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_LinearModels_SARIMA.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_LinearModels_SARIMA.py:


Timeseries with SARIMA
=======================================

In this script, a DLL SARIMA(0, 1, 1)x(1, 1, 1, 24) model is trained and compared against a statsmodels one on a time series dataset that contains linear trend, heteroscedasticity, seasonality etc.

.. GENERATED FROM PYTHON SOURCE LINES 7-67



.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_examples/LinearModels/images/sphx_glr_SARIMA_001.png
         :alt: SARIMA
         :srcset: /auto_examples/LinearModels/images/sphx_glr_SARIMA_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/LinearModels/images/sphx_glr_SARIMA_002.png
         :alt: Autocorrelation Function (ACF), Partial Autocorrelation Function (PACF)
         :srcset: /auto_examples/LinearModels/images/sphx_glr_SARIMA_002.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_examples/LinearModels/images/sphx_glr_SARIMA_003.png
         :alt: SARIMA
         :srcset: /auto_examples/LinearModels/images/sphx_glr_SARIMA_003.png
         :class: sphx-glr-multi-img





.. code-block:: Python

    import torch
    import matplotlib.pyplot as plt
    from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
    from statsmodels.tsa.statespace.sarimax import SARIMAX
    import numpy as np

    from DLL.MachineLearning.SupervisedLearning.LinearModels.TimeSeries import SARIMA


    np.seterr(over='ignore', divide='ignore', invalid='ignore', under='ignore')  # there is some bug in DLL SARIMA, which causes numerical errors, but does not effect the fit.

    n = 1000
    daily = torch.tensor([9181.231, 8966.770, 8803.231, 8635.086, 8588.066, 8624.506, 8805.777, 8849.321, 9044.870, 9126.868, 9295.427, 9440.119, 9483.297, 9526.187, 9552.341, 9763.771, 10143.724, 10098.868, 10184.532, 10175.405, 10060.573, 9783.887, 10079.360, 9959.197,])
    hours_per_day = 24
    n_days = 30
    n_hours = n_days * hours_per_day
    daily_pattern = torch.tile(daily / 10, (n_days,))
    torch.manual_seed(1)
    series = 2 * torch.arange(n_hours) + (0.3 + torch.arange(n_hours) / n) * daily_pattern + 10 * torch.randn(n_hours)

    p = 0.7
    split = int(n_hours * p)
    indicies = torch.arange(n_hours)
    series_train = series[:split]
    indicies_train = indicies[:split]
    series_test = series[split:]
    indicies_test = indicies[split:]

    order = (0, 1, 1)  # AR(0), since no peak at pacf in the start, SAR(1), since exponentially decreasing pacf
    seasonal_order = (1, 1, 1, hours_per_day)  # MA(1), since peak at 1 in acf, SMA(1), since peak at 24 in acf.
    model = SARIMA(series_train, order, seasonal_order)
    model.fit()
    preds, upper, lower = model.predict(n_ahead=n_hours - split)
    # print(model.summary())

    res_sm = SARIMAX(series_train.numpy(), order=order, seasonal_order=seasonal_order, trend="n").fit(disp=False)
    forecast_sm = res_sm.get_forecast(steps=n_hours - split)
    y_forecast_sm = forecast_sm.predicted_mean
    conf_int_sm = forecast_sm.conf_int()
    # print(res_sm.summary())

    plt.figure()
    diff_series = model._differentiate(series, order=order[1])
    diff_series = model._differentiate(diff_series, order=seasonal_order[1], lag=hours_per_day)
    plt.plot(diff_series, label="Differenced series")
    plt.legend()

    fig, ax = plt.subplots(2, 1)
    plot_acf(diff_series.numpy(), ax=ax[0], lags=100, title="Autocorrelation Function (ACF)")
    plot_pacf(diff_series.numpy(), ax=ax[1], lags=100, method="ywm", title="Partial Autocorrelation Function (PACF)")

    plt.figure()
    plt.plot(indicies_train, series_train, label="train")
    plt.plot(indicies_test, series_test, label="test")
    plt.plot(indicies_test, preds, label="DLL preds")
    plt.fill_between(indicies_test, lower, upper, alpha=0.2)
    plt.plot(indicies_test, y_forecast_sm, label="Statsmodel preds")
    plt.fill_between(indicies_test, conf_int_sm[:, 0], conf_int_sm[:, 1], alpha=0.2)
    plt.legend()
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 7.504 seconds)


.. _sphx_glr_download_auto_examples_LinearModels_SARIMA.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: SARIMA.ipynb <SARIMA.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: SARIMA.py <SARIMA.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: SARIMA.zip <SARIMA.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_