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The autoregressive (AR) model is a stochastic process modelling time series, which specifies the value of the series linearly in terms of the previous values.

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It's not strange you didn't calculate the AR(3) case. It's rather complicated! And no, there is no closed form for the AR(n)-case. For the AR(3) we start with the Yule-Walker equationsAR-model wikiped …
answered Jul 14 '15 by Stig Uteng