# PartialCorrelationFunction

PartialCorrelationFunction[data,hspec]

estimates the partial correlation function at lags hspec from data.

PartialCorrelationFunction[tproc,hspec]

represents the partial correlation function at lags hspec for the time series process tproc.

# Details

• PartialCorrelationFunction is also known as the partial autocorrelation function (PACF).
• PartialCorrelationFunction represents the correlation between x(t) and x(t+h), conditioned on x(u) for t<u<t+h, and x(t) representing tproc at time t.
• PartialCorrelationFunction[tproc,hspec] is defined only if tproc is a weakly stationary process.
• The process tproc can be any process such that WeakStationarity[tproc] gives True.
• 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,…}

# Examples

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## Basic Examples(3)

Estimate the partial correlation function at lag 2:

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

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Partial correlation function for an ARProcess:

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