Autocovariance

Computes the autocovariance of two columns vectors consistently with the var and cov functions.
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Updated 29 Mar 2012

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autocov computes the autocovariance between two column vectors X and Y with same length N using the Fast Fourier Transform algorithm from 0 to N-2.

The resulting autocovariance column vector acv is given by the formula:

acv(p,1) = 1/(N-p) * \sum_{i=1}^{N}(X_{i} - X_bar) * (Y_{i+p} - Y_bar)

where X_bar and Y_bar are the mean estimates:

X_bar = 1/N * \sum_{i=1}^{N} X_{i}; Y_bar = 1/N * \sum_{i=1}^{N} Y_{i}

It satisfies the following identities:
1. variance consistency: if acv = autocov(X,X), then acv(1,1) = var(X)
2. covariance consistence: if acv = autocov(X,Y), then acv(1,1) = cov(X,Y)

Cite As

Jacques Burrus (2024). Autocovariance (https://www.mathworks.com/matlabcentral/fileexchange/35915-autocovariance), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired by: autocov.m

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Version Published Release Notes
1.0.0.0