.. _sphx_glr_auto_examples_arima_example_seasonal_decomposition.py:


==========================================
Seasonal decomposition of your time-series
==========================================


This example demonstrates how we can use the ``decompose`` function to extract
the trend, seasonal, and random components of the time series and then
plot them all using the ``decomposed_plot`` function. We'll be plotting both
``additive`` and ``multiplicative`` examples of seasonality. To see the R
equivalent that inspired this example go `here <https://anomaly.io/seasonal-trend-decomposition-in-r/index.html>`_.

.. raw:: html

   <br/>




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


    *

      .. image:: /auto_examples/arima/images/sphx_glr_example_seasonal_decomposition_001.png
            :scale: 47

    *

      .. image:: /auto_examples/arima/images/sphx_glr_example_seasonal_decomposition_002.png
            :scale: 47





.. code-block:: python

    print(__doc__)

    # Author: Charles Drotar <drotarcharles@gmail.com>

    from pmdarima import arima
    from pmdarima import datasets
    from pmdarima import utils

    # #############################################################################

    # So what is happening when we call `decomposed`?
    # 1) The trend is extracted from the signal via a convolution using either a
    #    SMA or a user-defined filter.
    # 2) We remove the effects of the trend from the original signal by either
    #    subtracting its effects or dividing out its effects for `additive` or
    #    'multiplicative' types of decompositions, respectively. We then take the
    #    mean across all seasons to get the values for a single season. For m=4, we
    #    expect 4 values for a single season.
    # 3) We then create the seasonal series by replicating the single season
    #    until it is the same length of the trend signal.
    # 4) Lastly to get the random/noise elements of the signal we remove the effects
    #    of both the trend and seasonal series and we are now left with the
    #    variation of the original signal that is neither explainable by seasonal
    #    nor trend effects.
    #
    # This logic produces a named tuple of the original signal, trend, seasonal,
    # and random components. It is this named tuple that is passed to
    # `decomposed_plot`

    figure_kwargs = {'figsize': (6, 6)}  # set figure size for both examples

    #
    # ADDITIVE EXAMPLE : ausbeer
    #

    # Decompose the ausbeer dataset into trend, seasonal and random parts.
    # We subset to a small window of the time series.

    head_index = 17*4+2
    tail_index = 17*4-4
    first_index = head_index - tail_index
    last_index = head_index
    ausbeer = datasets.load_ausbeer()
    timeserie_beer = ausbeer[first_index:last_index]
    decomposed = arima.decompose(timeserie_beer, 'additive', m=4)

    # Plot the decomposed signal of ausbeer as a subplot

    axes = utils.decomposed_plot(decomposed, figure_kwargs=figure_kwargs,
                                 show=False)
    axes[0].set_title("Ausbeer Seasonal Decomposition")


    #
    # MULTIPLICATIVE EXAMPLE: airpassengers
    #

    # Decompose the airpassengers dataset into trend, seasonal and random parts.
    decomposed = arima.decompose(datasets.load_airpassengers(),
                                 'multiplicative', m=12)

    # Plot the decomposed signal of airpassengers as a subplot

    axes = utils.decomposed_plot(decomposed, figure_kwargs=figure_kwargs,
                                 show=False)
    axes[0].set_title("Airpassengers Seasonal Decomposition")

**Total running time of the script:** ( 0 minutes  0.058 seconds)



.. only :: html

 .. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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