BUILT-IN MATHEMATICA SYMBOL

# AbsoluteCorrelationFunction

AbsoluteCorrelationFunction[data, hspec]
estimates the absolute correlation function at lags hspec from data.

AbsoluteCorrelationFunction[proc, hspec]
represents the absolute correlation function at lags hspec for the random process proc.

AbsoluteCorrelationFunction[proc, s, t]
represents the absolute correlation function at times s and t for the random process proc.

## DetailsDetails

• AbsoluteCorrelationFunction is also known as the autocorrelation function.
• AbsoluteCorrelationFunction for a process proc with value at time t is given by:
•  Expectation[x[s]x[t]] for a scalar-valued process Expectation[x[s]x[t]] for a vector-valued process
• AbsoluteCorrelationFunction[proc, h] is defined only if proc is a weakly stationary process and is equivalent to AbsoluteCorrelationFunction[proc, 0, h].
• AbsoluteCorrelationFunction[{x1, ..., xn}, h] is equivalent to .
• When data is TemporalData containing an ensemble of paths, the output represents the average across all paths.
• The following specifications can be given for hspec:
•  at time or lag {max} unit spaced from 0 to {min,max} unit spaced from to {min,max,d} from to in steps of d {{1,2,...}} use explicit

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Estimate the absolute correlation function at lag 2:

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Sample the absolute correlation function for a random sample from an autoregressive time series:

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The absolute correlation function for a discrete-time process:

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The absolute correlation function for a continuous-time process:

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