Partial autocorrelation function: Difference between revisions

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== Examples ==

The following table summarizes the partial autocorrelation function of different models:<ref name=":1" /><ref name=":2">{{Cite book |last=Das |first=Panchanan |url=https://www.worldcat.org/oclc/1119630068 |title=Econometrics in Theory and Practice : Analysis of Cross Section, Time Series and Panel Data with Stata 15. 1 |date=2019 |publisher=Springer |year=2019 |isbn=978-981-329-019-8 |edition= |___location=Singapore |pages=294-299 |language=en |oclc=1119630068}}</ref>

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|[[Autoregressive model]]

|The partial autocorrelation for an AR(''p'') modelsmodel haveis nonzero partial autocorrelations for lags less than or equal to its order. In other words, the partial autocorrelation of an AR(''p'') processand is0 zero atfor lags greater than ''p''.

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|rowspan=2|[[Moving-average model]]

|The partial autocorrelation for MA(''q'') models exponentially decay to 0 as lags increase. If <math>\phi_{1,1} > 0</math>, the decaypartial isautocorrelation [[Oscillation (mathematics)|oscillatingoscillates]] or if <math>\phi_{1,1} <to 0</math>, the decay is geometric.

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|If <math>\phi_{1,1} < 0</math>, the partial autocorrelation [[Exponential decay|geometrically]] decays to 0.

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|[[Autoregressive–moving-average model]]

|An ARMA(''p'', ''q'') models have exponentially decayingmodel's partial autocorrelation geometrically decays to 0 but only after lags greater than ''p''.

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