.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/01_temporalTimeSeriesAnalysis/plot_movingAverageAutocovariance.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_01_temporalTimeSeriesAnalysis_plot_movingAverageAutocovariance.py>`
        to download the full example code.

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

.. _sphx_glr_auto_examples_01_temporalTimeSeriesAnalysis_plot_movingAverageAutocovariance.py:


Moving average analytical and estimated autocovariance
======================================================

.. GENERATED FROM PYTHON SOURCE LINES 7-9

Import requirements
-------------------

.. GENERATED FROM PYTHON SOURCE LINES 9-14

.. code-block:: Python


    import os
    import numpy as np
    import plotly.graph_objects as go








.. GENERATED FROM PYTHON SOURCE LINES 15-17

Define variables
-----------------

.. GENERATED FROM PYTHON SOURCE LINES 17-23

.. code-block:: Python


    srate = 1
    T = 100
    sigma = 1.0
    lags = np.arange(20)








.. GENERATED FROM PYTHON SOURCE LINES 24-27

Create white noise
------------------


.. GENERATED FROM PYTHON SOURCE LINES 27-32

.. code-block:: Python


    time = np.arange(0, T, 1.0/srate)
    N = len(time)
    w = np.random.normal(loc=0, scale=sigma, size=N)








.. GENERATED FROM PYTHON SOURCE LINES 33-36

Create moving average time series
---------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 36-42

.. code-block:: Python

    ma = np.empty(len(w), dtype=np.double)
    ma[0] = (w[0] + w[1]) / 3
    for i in range(1, len(w)-1):
        ma[i] = (w[i-1] + w[i] + w[i+1]) / 3
    ma[-1] = (w[-2] + w[-1]) / 3








.. GENERATED FROM PYTHON SOURCE LINES 43-46

Estimate autocovariance
-----------------------


.. GENERATED FROM PYTHON SOURCE LINES 46-64

.. code-block:: Python


    estAcov = np.zeros(len(lags))
    anaAcov = np.zeros(len(lags))
    maMu = np.mean(ma)
    for h in lags:
        if h == 0:
            anaAcov[h] = 3.0 / 9 * sigma**2
            xs = ma - maMu
            xt = ma - maMu
        else:
            xs = ma[h:] - maMu
            xt = ma[:-h] - maMu
            if h == 1:
                anaAcov[h] = 2.0 / 9 * sigma**2
            elif h == 2:
                anaAcov[h] = 1.0 / 9 * sigma**2
        estAcov[h] = np.mean(xs * xt)








.. GENERATED FROM PYTHON SOURCE LINES 65-68

Plot moving average time series, true and estimated autocovariance
------------------------------------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 68-95

.. code-block:: Python


    fig = go.Figure()
    trace = go.Scatter(x=time, y=ma, mode="lines+markers")
    fig.add_trace(trace)
    fig.update_layout(xaxis=dict(title="Time (sec)"), yaxis=dict(title="x"))

    if not os.path.exists("figures"):
        os.mkdir("figures")

    fig.write_html(f"figures/movingAverageSamplesN{T}.html")
    fig.write_image(f"figures/movingAverageSamplesN{T}.png")

    fig = go.Figure()
    trace = go.Scatter(x=lags, y=anaAcov, mode="lines+markers", name="analytical")
    fig.add_trace(trace)
    trace = go.Scatter(x=lags, y=estAcov, mode="lines+markers", name="estimated")
    fig.add_trace(trace)
    fig.update_layout(title=f"N={T}", xaxis=dict(title="Lag (samples)"),
                      yaxis=dict(title="Autocovariance"))

    if not os.path.exists("figures"):
        os.mkdir("figures")

    fig.write_html(f"figures/movingAverageAutoCovN{T}.html")
    fig.write_image(f"figures/movingAverageAutoCovN{T}.png")

    fig





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.. _sphx_glr_download_auto_examples_01_temporalTimeSeriesAnalysis_plot_movingAverageAutocovariance.py:

.. only:: html

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

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

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

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


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