# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE 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.
• The following specifications can be given for hspec:
•  τ at time or lag τ {τmax} unit spaced from 0 to {τmin,τmax} unit spaced from to {τmin,τmax,dτ} from to in steps of dτ {{τ1,τ2,…}} use explicit
• AbsoluteCorrelationFunction[{x1,,xn},h] is equivalent to .
• When data is TemporalData containing an ensemble of paths, the output represents the average across all paths.
• 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
• The symbol represents KroneckerProduct.
• AbsoluteCorrelationFunction[proc,h] is defined only if proc is a weakly stationary process and is equivalent to AbsoluteCorrelationFunction[proc,h,0].
• The process proc can be any random process such as ARMAProcess and WienerProcess.

## 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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