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How would you determine the p and q lags in ARIMA models?

Stochastic
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palmer
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    In practice, it is often done in an automated way. Many models with different p, q, and d values are fit to the data and the goodness of their fit is compared using something like AIC which weighs both the goodness of fit and the complexity of the model. There are other ways to choose appropriate models using the data plot, ACF, PACF, and various model diagnostics. – Ryan Volpi May 31 '20 at 20:40

1 Answers1

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As a rule of thumb, these are determined by when the lags of the ACF and PACF cut off.

Determining p and q

If the ACF cuts off after lag 2, a MA(2) will be suggested (q=2). If the PACF cuts off at lets say lag 3, the suggestion will be an AR(3) (p=3) model. More of that here.
I often try an ARMA(1,1) model if the ACF or PACF decay over time, however a slowly decaying ACF may point to non-stationarity, so be watchful for that.

Ideal model

The less parameters you have, the more parsimonious (less complex) your model is. (I simply like to try the ARMA(1,1) since it only has two parameters). @Ryan mentioned the AIC in his comment, which penalizes models with more parameters. You ideally want to find a model with as few parameters as possible, with them still being significant, a low AIC/SBC and one whose residuals are white noise.

Supplementary post

Have said all this, I think the answer in this post explains very well what you were questioning.

Hope this answers your question :)

Stochastic
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