# Overview of selection method for p-order of AR($p$) model [closed]

I would like to get an overview over the most common methods for estimating the lag order of an AR($p$) process.

The common literature states:

1. Akaike information criterion (AIC)
2. Bayesian information criterion (BIC)
3. Hannan–Quinn information criterion (HQC)
4. Akaike's final prediction error (FPE) criterion
5. Criterion autoregressive transfer function (CAT) %of Parzen.
6. Minimum description length (MDL)
7. Resiudal variance (RV) method

I kindly ask to refer to other methods and maybe highlight their advantages compared to AIC or BIC.

## closed as too broad by whuber♦Sep 16 at 18:51

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• This has been discussed in many threads before, you will certainly find a number of relevant answers if you do a thorough search. – Richard Hardy Sep 6 '16 at 16:11

You can use auto-correlation plots/partial auto-correlation plots. See the Box-Jenkins wikipedia page. The idea is that if you process is an AR(q) process, after q lags the partial-autocorrelation plot, should go to zero. Partial-autocorrelation plot basically is a plot that compares the correlation of $x(t)$ and $x(t+k)$, except you only take the component of $x(t)$ and $x(t+k)$ that is orthogonal to all the intervening lags $(x(t)...x(t+k-1))$ (ie you take the residual of a regression). You test when that plot dies down to zero--using confidence intervals for example--and that gives you the number of lags.