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If I have given two time series, an MA and an AR how can I determine who is who? I know how to do it with a correlogram, i know that if the autocorrelation goes straight to zero after q lags it is a MA, and if it goes exponentially against zero it is a AR.

See example http://www.diskusjon.no/uploads/monthly_11_2016/post-122992-0-13646900-1480525320.png

Richard Hardy
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TheNarsisisst
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2 Answers2

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Since all AR models can be re-presented as an MA model , I will presume from the plot that in this case the MA model is not the rational inverse of the AR model. It would appear that the red line is an AR model with a negative coefficient suggesting a flip-flop graph.

IrishStat
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The example you link to ask you do decide which series is AR(1) and which series is MA(1). For an AR(1) model autocorrelation tails off geometrically whereas for an MA(1) model there is no autocorrelation for lags$\ge2$. Based on this you can clearly see that series 1 is AR(1) and series 2 is MA(1).

Jarle Tufto
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  • Ok, så since Series 1 is an AR(1), the autocorrelation tails of geometrically against zero, and that why we can se some pattern? For example if we look between time 16 and 26 its always climbing. Sine series 2 is an MA(1), the autocorrelation will be zero after 1 lag, and therefor there will be no clear pattern in the series? – TheNarsisisst Nov 30 '16 at 22:32
  • Yes, that's right, no autocorrelation for MA(1) except for lag 1. – Jarle Tufto Nov 30 '16 at 22:46