# 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.

# Details • 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 τmax {τmin,τmax} unit spaced from τmin to τmax {τmin,τmax,dτ} from τmin to τmax in steps of dτ {{τ1,τ2,…}} use explicit {τ1,τ2,…}
• 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 x[t] 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.

# Examples

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## Basic Examples(4)

Estimate the absolute correlation function at lag 2:

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

 In:= In:= Out= The absolute correlation function for a discrete-time process:

 In:= Out= In:= Out= The absolute correlation function for a continuous-time process:

 In:= Out= In:= Out= ## Possible Issues(1)

Introduced in 2012
(9.0)