# Lag order selection for Toda-Yamamoto procedure (Granger causality)

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.

• What is the nature of your time series data and what is the frequency? Apr 20 '15 at 10:23
• The data are on interest rates with monthly frequency and number of observations ranging from 100 to 150 Apr 23 '15 at 12:36
• 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. Apr 24 '15 at 18:38
• 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? Apr 25 '15 at 13:27

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.