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  • Last update: 5 years ago
  • Total downloads: 12
  • Operating system: Linux, Mac OS X, Win All, BSD, Solaris
  • Publisher: Jacques Burrus
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scripts default iconAutocovariance (Scripts) Publisher's description

Computes the autocovariance of two columns vectors consistently with the var and cov functions.

Computes the autocovariance of two columns vectors consistently with the var and cov functions.
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)

System Requirements:

No special requirements.
Program Release Status: Minor Update
Program Install Support: Install and Uninstall

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