maths.autocorrelation
=====================

.. py:module:: maths.autocorrelation

.. autoapi-nested-parse::

   Autocorrelation measures the correlation of a signal with a delayed
   copy of itself. It is widely used in time series analysis, signal
   processing, and statistics.

   Reference: https://en.wikipedia.org/wiki/Autocorrelation



Attributes
----------

.. autoapisummary::

   maths.autocorrelation.data


Functions
---------

.. autoapisummary::

   maths.autocorrelation.autocorrelation


Module Contents
---------------

.. py:function:: autocorrelation(data: list[float], lag: int) -> float

   Calculate the autocorrelation of a time series at a given lag.

   :param data: A list of numerical values representing the time series.
   :param lag: The number of time steps to shift the series.
   :return: The autocorrelation coefficient at the given lag.

   >>> round(autocorrelation([1, 2, 3, 4, 5], 1), 4)
   0.4
   >>> round(autocorrelation([1, 2, 3, 4, 5], 0), 4)
   1.0
   >>> autocorrelation([1, 2, 3], 5)
   Traceback (most recent call last):
       ...
   ValueError: Lag must be less than the length of the data.


.. py:data:: data
   :value: [1, 2, 3, 4, 5, 4, 3, 2, 1]