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

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

.. _sphx_glr_auto_examples_01_temporalTimeSeriesAnalysis_plot_whiteNoiseAutocorrelation.py:


White noise analytical and estimated autocorrelation, and 95% confidence interval
=================================================================================

.. 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 = 10000
    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

Estimate autocorrelation
------------------------


.. GENERATED FROM PYTHON SOURCE LINES 36-50

.. code-block:: Python


    anaAcor = np.zeros(len(lags))
    anaAcor[0] = sigma
    estAcor = np.zeros(len(lags))
    wMu = np.mean(w)
    wSTD = np.std(w)
    for h in lags:
        if h == 0:
            estAcor[h] = 1.0
        else:
            xs = w[h:] - wMu
            xt = w[:-h] - wMu
            estAcor[h] = np.mean(xs * xt)/wSTD








.. GENERATED FROM PYTHON SOURCE LINES 51-54

Plot white noise analytical and estimated autocorrelations plus 95% confidence interval
---------------------------------------------------------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 54-72

.. code-block:: Python


    fig = go.Figure()
    trace = go.Scatter(x=lags, y=anaAcor, mode="lines+markers", name="analytical")
    fig.add_trace(trace)
    trace = go.Scatter(x=lags, y=estAcor, mode="lines+markers", name="estimated")
    fig.add_trace(trace)
    fig.add_hline(y=1.96/np.sqrt(N), line=dict(dash="dash"))
    fig.add_hline(y=-1.96/np.sqrt(N), line=dict(dash="dash"))
    fig.update_layout(title=f"N={T}", xaxis=dict(title="Lag (samples)"),
                      yaxis=dict(title="Autocorrelation"))

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

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

    fig





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

   **Total running time of the script:** (0 minutes 0.096 seconds)


.. _sphx_glr_download_auto_examples_01_temporalTimeSeriesAnalysis_plot_whiteNoiseAutocorrelation.py:

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

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

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


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