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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_examples_decomposition_plot_ssa.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_decomposition_plot_ssa.py:


==========================
Singular Spectrum Analysis
==========================
Signals such as time series can be seen as a sum of different signals such
as trends and noise. Decomposing time series into several time series can
be useful in order to keep the most important information. One decomposition
algorithm is Singular Spectrum Analysis. This example illustrates the
decomposition of a time series into several subseries using this algorithm and
visualizes the different subseries extracted.
It is implemented as :class:`pyts.decomposition.SingularSpectrumAnalysis`.

.. GENERATED FROM PYTHON SOURCE LINES 13-56



.. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_ssa_001.png
   :alt: Singular Spectrum Analysis
   :srcset: /auto_examples/decomposition/images/sphx_glr_plot_ssa_001.png
   :class: sphx-glr-single-img





.. code-block:: default


    # Author: Johann Faouzi <johann.faouzi@gmail.com>
    # License: BSD-3-Clause

    import numpy as np
    import matplotlib.pyplot as plt
    from pyts.decomposition import SingularSpectrumAnalysis

    # Parameters
    n_samples, n_timestamps = 100, 48

    # Toy dataset
    rng = np.random.RandomState(41)
    X = rng.randn(n_samples, n_timestamps)

    # We decompose the time series into three subseries
    window_size = 15
    groups = [np.arange(i, i + 5) for i in range(0, 11, 5)]

    # Singular Spectrum Analysis
    ssa = SingularSpectrumAnalysis(window_size=15, groups=groups)
    X_ssa = ssa.fit_transform(X)

    # Show the results for the first time series and its subseries
    plt.figure(figsize=(16, 6))

    ax1 = plt.subplot(121)
    ax1.plot(X[0], 'o-', label='Original')
    ax1.legend(loc='best', fontsize=14)

    ax2 = plt.subplot(122)
    for i in range(len(groups)):
        ax2.plot(X_ssa[0, i], 'o--', label='SSA {0}'.format(i + 1))
    ax2.legend(loc='best', fontsize=14)

    plt.suptitle('Singular Spectrum Analysis', fontsize=20)

    plt.tight_layout()
    plt.subplots_adjust(top=0.88)
    plt.show()

    # The first subseries consists of the trend of the original time series.
    # The second and third subseries consist of noise.


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

   **Total running time of the script:** ( 0 minutes  3.365 seconds)


.. _sphx_glr_download_auto_examples_decomposition_plot_ssa.py:

.. only:: html

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


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

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

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

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


.. only:: html

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

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