Thank you, but all criteria pick lag 1

Dear Suleyman,

what is the frequency of data you are analyzing - quarterly or annual - and how many observations you have? Some information criteria, like SC, have better performance on small samples. Since all criteria suggest using lag 1, I think that you should use lag 1 and to conclude that there is no cointegration. Of course, if all other conditions are fulfilled and residual diagnostics is ok (if the model is well suited).

Regards,

Vladimir

Totally agree with Vladimir, above. The stats and criteria are only informed indications/suggestions and of course they rely on the amount of information available. Since we are only talking for 27 observations (if the data are annual), 108 (if quarterly), then there is a chance there are not enough observations as the correct lag length to be correctly guessed. In that case, I would try the lag = 2.

Remark 1: Have you examined the lag length of the three series separately? If even one of them has lag length = 2 that would be a additional argument.

Remark 2: Its usually the annual economic series which indicate lag length = 1. In that case you have only 27 observations, therefore degrees of freedom may be insufficient for VECM with 2 lags. On the other hand, if using quarterly data seasonality treatment should be necessary.

Thank you very much for your response, my variables are in annual basis.

Thank you Pandelis Mitsis for your remarks.

@ Vladimir Mihajlovic

I also run VAR using selected Lag 1, but the diagnostic test for residue is that; Residue are not Multivariate Normal, (not normally distributed) but this work well when using Lag 2

When using Lag 2 in var model, I accept the null hypothesis that residue are multivariate normal!!

Please advice me!

Most of the diagnostics, especially the Jarque-bera test, are known to under-perform with a small number of observations - e.g. less than 100.

With a VAR with only 27 observations, I would advise you to choose the model with the more meaningful results for the topic of your analysis and make sure you emphasize in the text that the small span of data was a major restriction in using a more elaborate model in your empirical analysis.

Good Luck!

Thank you very much @Pandelis Mitsis.

I'll work on your suggestion.

Thank you

It is useful to use information criteria (such as AIC and Schwarz) to determine an initial lag length. However, ultimately there should be no evident misspecification and, as a minimum, you should test for autocorrelation. You would probably want the shortest VAR lag length (for efficiency) that avoids evident autocorrelation (or misspecification more generally). If you use a VAR in levels to find the initial lag length and the data are nonstationary you should convert the model into a VECM (in preparation for cointegration testing) and check the VECM for evident autocorrelation (misspecification). If there is no cointegration using the appropriate lag length there is no cointegration.

The validation of your model is a balance between several performance critiria such as information criteria, analysis of the model residuals (white noise), the significance of your most important variables in the model.... you are the one to make a balance between all these according to your problematic...

Thank you all for your response, I really appreciate that!

Use Lag 2 or more appropriately lag order of two but check for autocorrelation!

Hi

I'm not sure I understood your problem. How could you use VAR while your variables are integrated? I(1)? If your objectif is to test cointegration I agree with Stewart your should use a VECM specifishoulder and information criteria are always useful.