Partial autocorrelation function: Difference between revisions

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AR models have nonzero partial autocorrelations for lags less than or equal to its order. In other words, the partial autocorrelation of an AR(''p'') process is zero at lags greater than ''p''.

For [[Moving -average model|moving average (MA)]] models, their partial autocorrelation exponentially decays to 0. For MA models that have <math>\phi_{1,1} > 0</math>, the decay is [[Oscillation (mathematics)|oscillating]] and the other models with <math>\phi_{1,1} < 0</math> have geometric decay.

The partial autocorrelation function of an [[ARMA model|ARMA(''p'', ''q'') model]] also exponentially decays but only after lags greater than ''p''.<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>