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

    Click :ref:`here <sphx_glr_download_auto_examples_stats_plot_stats_stationary.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_stats_plot_stats_stationary.py:


====================================================
Identify stationary time-series using unit root test
====================================================

This example illustrates how to identify stationary time-series (i.e.
time-series with constant statistical properties such as mean, variance etc.).
Here, we are going to use the Augmented Dickey-Fuller test.


.. code-block:: default

    import numpy as np

    from tensorpac.stats import test_stationarity

    import matplotlib.pyplot as plt







Define a random dataset
##############################################################################
 Let first create a random dataset and change temporal properties


.. code-block:: default


    n_epochs = 8   # number of epochs
    n_times = 200  # number of time points
    sf = 128.

    # create a reproducable random dataset
    rng = np.random.RandomState(1)
    data = rng.rand(n_epochs, n_times)
    time = np.arange(n_times) / sf

    # if we run the test on this random dataset, every epochs are going to be found
    # as stationary as statistical properties are constant across time. Hence, we
    # can introduce some randomness into this dataset to illustrate the sensibility
    # of the test

    titles = {0: "constant offset", 1: "increasing linear trend",
              2: "decreasing linear trend", 3: "constant oscillations",
              4: "offset on second half", 5: "divide by 2 first half amplitude",
              6: "modulated oscillations", 7: "random signal"}

    # Epoch 0 : constant offset
    data[0, :] += 10.
    data[1, :] += np.linspace(0, 1, n_times)
    data[2, :] += np.linspace(1, 0, n_times)
    data[3, :] += np.sin(2 * np.pi * 4 * time)
    data[4, 100:] += 30.
    data[5, 0:100] /= 2
    data[6, :] += np.sin(2 * np.pi * 4 * time) * np.linspace(1, 2, n_times)







Compute the statistical test
##############################################################################
 now, run the Augmented Dickey-Fuller test in order to identify which trials
 are statisticaly considered as stationary


.. code-block:: default


    df = test_stationarity(data, p=0.05)
    print(df)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

        Epochs  ...   CV (1%)
    0  epoch 0  ... -3.463815
    1  epoch 1  ... -3.465244
    2  epoch 2  ... -3.466005
    3  epoch 3  ... -3.466398
    4  epoch 4  ... -3.463645
    5  epoch 5  ... -3.465059
    6  epoch 6  ... -3.466398
    7  epoch 7  ... -3.463645

    [8 rows x 6 columns]



Plot each trial
##############################################################################
 finally, plot color-coded time-series (green : stationary,
 red: non-stationary)


.. code-block:: default


    colors = {True: 'green', False: 'red'}

    is_stationary = df["Stationary"]

    plt.figure(figsize=(18, 8))
    for k in range(n_epochs):
        plt.subplot(2, 4, k + 1)
        plt.plot(data[k, :], color=colors[is_stationary[k]])
        plt.title(titles[k], fontweight='bold')
    plt.tight_layout()
    plt.show()



.. image:: /auto_examples/stats/images/sphx_glr_plot_stats_stationary_001.png
    :class: sphx-glr-single-img





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

   **Total running time of the script:** ( 0 minutes  1.650 seconds)


.. _sphx_glr_download_auto_examples_stats_plot_stats_stationary.py:


.. only :: html

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



  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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


.. only:: html

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

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