# Lag Exclusion test for VAR - What are the null and alternative hypotheses?

everyone.

I ran a lag exclusion test for my VAR model on EViews and arrived at the Chi-squared test statistics as shown in the image linked below. Could someone please tell me what exactly are the null and alternative hypotheses for the individual and joint tests being used here and how should I decide which of these should I use, the individual or the joint test? Also, how can I find which lags are insignificant and how should I proceed to remove them from my model?

Best,

Max

You should use the joint null hypothesis against the alternative. Null hypothesis: the lag length that is used estimating the VAR model. Alternative hypothesis: another lag length that should be used. For instance, when you use 2 lags, the p-value = 0.0096. Decision: you can reject lag length 2 in favor of lag 3. By doing so you are taking a decision with an almost zero percent probability of making a mistake. When you use 3 lags, the p-value of the Chi square statistic is 0.11. This means, you can't reject lag length 3 in favor of lag 4. If you do that the probability of making an error is almost 11 percent.

• Isn't the $H_0$ that the coefficient for a particular variable (or all variables jointly) at a particular lag equals zero? Thus the test would be not about lag length but rather about the inclusion/exclusion of a particular lag in this VAR(4) model? Dec 23, 2018 at 20:23
• Eviews manual says it is joint significance of all endogenous variables at that lag. This answer is misleading. Nov 27, 2019 at 21:38

Staying at the image,

in the square brackets of the first 3 columns there are the p-values for hypothesis referred on 3 parameters each. For example in position $$[1,1]$$ we have $$[0.211067]$$ that is about significance of DLCONS lag1 parameters, valid for the 3 dependent variable jointly. In the last column we have the test about the lag of order $$i=1,2,3,4,5$$ for all 3 predictors and all 3 dependent variables jointly, 9 parameters each.

how can I find which lags are insignificant and how should I proceed to remove them from my model?

Your question sound like: what's the best lag order for my VAR?

From above table you do not have explicit answer, even if lag 5 probably can be removed. There are several alternatives about that, among them there are sequential hypothesis testing procedures and information criteria like BIC and AIC. Here there is a related presentation: https://homepage.univie.ac.at/robert.kunst/pres07_var_abdgunyan.pdf