Solved – LM test interpretation in VAR – a joint hypotheses test? (In EViews)

autocorrelationvector-autoregression

This question is about how to interpret LM test in VAR.

For example, under VAR with lag 1, the LM test shows 

lags----LM-stat----Prob
1-------34.73------0.0043
2-------21.76------0.1508

Oh! auto-correlation in lag 1! So, I rerun VAR with 1 more lag. Then the result of LM test under VAR with 2 lags is

lags---LM-stat-----Prob 
1------31.37932----0.0120
2------10.62227----0.8322
3------20.56224----0.1960

Now my VAR has autocorrelation or not? According to my knowledge (i dont have much technical knowledge), standard LM test is a joint test. But the way EViews manual's description looks like LM test under VAR is not a joint hypotheses test. Which means, in my case, I still suffer auto-correlation at lag 1 under VAR(2), RIGHT?

Say, even I have a VAR(6) system, if the LM test result is:

Lags---LM-Stat-----Prob
1------34.43359----0.0047
2------24.91163----0.0714
3------20.13258----0.2143
4------9.748399----0.8794
5------16.69178----0.4058
6------22.46036----0.1289
7------11.65195----0.7676

I still suffer autocorrelation at lag 1, right?

Best Answer

According to the EViews manual, Autocorrelation LM Test [r]eports the multivariate LM test statistics for residual serial correlation up to the specified order. So it is a joint test just as it should be (because of up to the specified order rather than at some particular order or the like). Where did you find written otherwise?

Now my VAR has autocorrelation or not?

At lag 1 there is rather strong evidence against no autocorrelation ($p$-value of 1.2%) but less so when you take the first two or the first three lags jointly ($p$-values of 83.2% and 19.6%, respectively).

I still suffer auto-correlation at lag 1 under VAR(2), RIGHT?

Yes, you do, as explained above.

I still suffer autocorrelation at lag 1, right?

Yes, you do, because here the $p$-value is just 0.47%.

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