.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/decomposition/plot_auto_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_auto_ssa.py>`
        to download the full example code

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

.. _sphx_glr_auto_examples_decomposition_plot_auto_ssa.py:


============================================================
Trend-Seasonal decomposition with Singular Spectrum Analysis
============================================================
Time series can be composed of three different subseries:
trend, seasonal and noise. Decomposing time series into these components
can be useful in order to characterize the underlying signal. One decomposition
algorithm is Singular Spectrum Analysis. This example illustrates the
decomposition of a time series into the three subseries using the automatic
grouping of the SSA-components and visualizes the results depending
on the selected parameters.
It is implemented as :class:`pyts.decomposition.SingularSpectrumAnalysis`.

.. GENERATED FROM PYTHON SOURCE LINES 14-72



.. image-sg:: /auto_examples/decomposition/images/sphx_glr_plot_auto_ssa_001.png
   :alt: Singular Spectrum Analysis, lower_frequency_bound: 0.075, lower_frequency_contribution: 0.85, lower_frequency_bound: 0.01, lower_frequency_contribution: 0.85, lower_frequency_bound: 0.01, lower_frequency_contribution: 0.98
   :srcset: /auto_examples/decomposition/images/sphx_glr_plot_auto_ssa_001.png
   :class: sphx-glr-single-img





.. code-block:: default


    # Author: Lucas Plagwitz <lucas.plagwitz@uni-muenster.de>
    # License: BSD-3-Clause

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

    # Parameters
    n_samples, n_timestamps = 3, 128

    X_cbf, y = make_cylinder_bell_funnel(n_samples=10, random_state=42,
                                         shuffle=False)
    X_period = 3 * np.sin(np.arange(n_timestamps))

    X = X_cbf[:, :n_timestamps] + X_period

    # We decompose the time series into three subseries
    window_size = 20
    # Singular Spectrum Analysis
    ssa = SingularSpectrumAnalysis(window_size=window_size, groups="auto")
    X_ssa = ssa.fit_transform(X)

    # Show the results for different frequency-parameters
    plt.figure(figsize=(16, 12))

    ax1 = plt.subplot(221)
    ax1.plot(X[0], 'o-', label='Original')
    ax1.plot(X_period, 'o-', label='periodic')
    ax1.legend(loc='best', fontsize=14)
    ax1.set_ylim([np.min(X[0])*1.1, np.max(X[0])*1.1])

    params = [(0.01, 0.85), (0.01, 0.98)]

    for idx in range(3):
        ax = plt.subplot(222 + idx)
        labels = ["trend", "periodic", "residual"]
        for i in range(3):
            ax.plot(X_ssa[0, i], 'o--', label=labels[i])
        ax.legend(loc='best', fontsize=14)
        ax.set_ylim([np.min(X[0])*1.1, np.max(X[0])*1.1])
        ax.set_title(f"lower_frequency_bound: {ssa.lower_frequency_bound}, "
                     f"lower_frequency_contribution: "
                     f"{ssa.lower_frequency_contribution}")

        if idx > 1:
            continue
        ssa = SingularSpectrumAnalysis(window_size=window_size, groups="auto",
                                       lower_frequency_bound=params[idx][0],
                                       lower_frequency_contribution=params[idx][1])
        X_ssa = ssa.fit_transform(X)

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

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


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

   **Total running time of the script:** ( 0 minutes  0.853 seconds)


.. _sphx_glr_download_auto_examples_decomposition_plot_auto_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_auto_ssa.py <plot_auto_ssa.py>`

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

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


.. only:: html

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

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