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I am trying to determine the optimal lag order in a two-equation VAR as follows:

  1. choose the lag order based on information criteria;
  2. estimate the model using # of lags determined above and test for autocorrelation in errors (up to order 4): if auctocorrelation is found at any of the orders I add one additional lag and test again (lags are added until autocorrelation disappears).

Is this approach sensible? Also, given that I have limited sample size (around 150 observations), what is the maximum number of lags I should allow?

The goal is to use the model for testing Granger causality using the Toda-Yamamoto procedure.

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  • $\begingroup$ What is the nature of your time series data and what is the frequency? $\endgroup$
    – fredrikhs
    Commented Apr 20, 2015 at 10:23
  • $\begingroup$ The data are on interest rates with monthly frequency and number of observations ranging from 100 to 150 $\endgroup$
    – user2626097
    Commented Apr 23, 2015 at 12:36
  • $\begingroup$ Using information criteria (IC) for lag length selection is justified in the sense that the IC-suggested lag order strikes a balance between underfitting and overfitting. Depending on your purposes (what the model will be used for), you could just stick to what the IC suggest. Trying to enlarge the model to reduce autocorrelation in the errors will come at an expense of estimation imprecision due to the limited sample size. But this is a pretty general argument; perhaps you have valid reasons for really wanting to get rid of the autocorrelation even at the expense of overfitting. $\endgroup$
    – Richard Hardy
    Commented Apr 24, 2015 at 18:38
  • $\begingroup$ My purpose is to perform Granger causality test using Toda-Yamamoto test and depending on the results possible also Johansen test, so in that case I actually must actually remove the autocorrelation, or can I still rely on IC? $\endgroup$
    – user2626097
    Commented Apr 25, 2015 at 13:27

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The Toda-Yamamoto procedure for testing Granger causality is described very clearly and explicitly as a 13-step sequence in Dave Giles' blog post "Testing for Granger causality". There is no point in reiterating it here.

Regarding lag order selection, Dave Giles suggests starting with the lag selected by an information criterion such as AIC or BIC. He then emphasizes the need to ensure that there is no serial correlation in the residuals ("If need be, increase $p$ until any autocorrelation issues are resolved"). Therefore, your approach seems fine.

Regarding the maximum lag order, I do not have a precise answer. You should be cautious not to use too small a maximum lag to leave enough room for AIC/BIC to do the job. I would select a pretty large maximum lag and leave the rest for AIC/BIC. AIC/BIC would normally strike a good balance so that even if you allow for a really high maximum lag, it would not be selected and no harm would be caused.

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