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

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

.. _sphx_glr_auto_examples_01_temporalTimeSeriesAnalysis_plot_randomWalkWithDriftExample.py:


Generation of a random walk with drift time series
==================================================

.. 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 17-24

.. code-block:: Python


    srate = 1
    T = 200 # sec
    sigma = 1.0
    delta0 = 0.0
    delta1 = .2








.. GENERATED FROM PYTHON SOURCE LINES 25-28

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


.. GENERATED FROM PYTHON SOURCE LINES 28-34

.. code-block:: Python


    time = np.arange(0, T, 1.0/srate)
    N = len(time)
    w0 = np.random.normal(loc=0, scale=sigma, size=N)
    w1 = np.random.normal(loc=0, scale=sigma, size=N)








.. GENERATED FROM PYTHON SOURCE LINES 35-38

Create random walk with noise time series
-----------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 38-47

.. code-block:: Python


    rwWithDrift0 = np.empty(N, dtype=np.double)
    rwWithDrift1 = np.empty(N, dtype=np.double)
    rwWithDrift0[0] = 0.0
    rwWithDrift1[0] = 0.0
    for i in range(1, N):
        rwWithDrift0[i] = delta0 + rwWithDrift0[i-1] + w0[i]
        rwWithDrift1[i] = delta1 + rwWithDrift1[i-1] + w1[i]








.. GENERATED FROM PYTHON SOURCE LINES 48-51

Plot random noise with drift time series
----------------------------------------


.. GENERATED FROM PYTHON SOURCE LINES 51-74

.. code-block:: Python


    fig = go.Figure()
    trace = go.Scatter(x=time, y=rwWithDrift0, mode="lines+markers",
                       line=dict(color="blue"), name=r"$\delta=0.0$")
    fig.add_trace(trace)
    trace = go.Scatter(x=time, y=rwWithDrift1, mode="lines+markers",
                       line=dict(color="black"), name=r"$\delta=0.2$")
    fig.add_trace(trace)
    trace = go.Scatter(x=[0, T], y=[0, 0], line=dict(color="blue", dash="dot"),
                       mode="lines", showlegend=False)
    fig.add_trace(trace)
    trace = go.Scatter(x=[0, T], y=[0, delta1*T], line=dict(color="black", dash="dot"),
                       mode="lines", showlegend=False)
    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("figures/randomWalkWithDrift.html")
    fig.write_image("figures/randomWalkWithDrift.png")

    fig





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.. _sphx_glr_download_auto_examples_01_temporalTimeSeriesAnalysis_plot_randomWalkWithDriftExample.py:

.. only:: html

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

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

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

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

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


.. only:: html

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

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