Take the 2-minute tour ×
Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It's 100% free, no registration required.

When preforming Johansen Cointegration test for 2 time series (the simple case) you need to decide the lag you want to use. Doing the test for different lags return different results: for some lag levels the null hypothesis can be rejected but for others it can't.

My question is what is the right method based on the input data to decide what lag I need to use when preforming the Johansen Test?

p.s. I submitted this question to quant.stackexchange but some suggested it is better fit to this group.

share|improve this question
add comment

3 Answers

AIC or SBC could be used to help you decide what lag. The URCA package in R recommends selecting the lag having minimum AIC or SBC.

share|improve this answer
    
It should be added that the information criteria should be calculated on VAR model in levels. –  mpiktas Dec 30 '12 at 8:01
add comment

You are correct. The weakness of Johansen approach is that it is sensitive to the lag length. So, the lag length should be determined in a systematic manner. Following is the normal process used in the literature.

a. Choose maximum lag length "m" for VAR model. Usually, for annual data this is set to 1, for quarterly data this is set to 4, and for monthly data this is set to 12.

b. Run the VAR model in level. For example, if the data is monthly, run the VAR model for lag lengths 1,2, 3,....12.

c. Find the AIC (Akaike information criterion) and SIC (Schwarz information criterion) [ there are also other criteria such as HQ (Hannan-Quin information criterion), FPE (Final prediction error criterion) but AIC and SIC are mostly used) for the VAR model for each lag length. Choose the lag length that minimizes AIC and SIC for the VAR model. Note that SIC and AIC may give conflicting results.

d. Finally, you MUST confirm that for the lag length you selected in step c, the residuals of the VAR model are not correlated [use Portmanteau Tests for autocorrelations]. You may have to modify the lag length, if there is the autocorrelation. Usually, beginners in time series econometrics tend to skip step d.

e. For the cointegration, the lag length is the lag length chosen from step d minus one (since we are running the model in first difference now, unlike in level when we used VAR to decide the lag length).

share|improve this answer
    
Do you have an example of a published paper that sets the maximum lag for quarterly data to 4? –  Jase Dec 31 '12 at 4:02
    
@Jase: Right now, no! I would suggest you to read p.313 Applied Econometrics Time Series (Paul Enders, First edition). Enders suggests to start with 12 lags for quarterly (unlike 4, in the above answer). His argument is based on the theory and data availability. For example, if there is theoretical justification that the variable may have influence up to two years (and provided that there is data for, say like 30 years) one can start with maximum lag of eight). Where there is no clear theory, one can use max lag length of 4 for quarterly data. –  Metrics Dec 31 '12 at 4:39
    
If I have exogenous variables (that enter as levels because the levels are $I(0)$) in my VECM, how do I select lag length of this VECM? –  Jase Dec 31 '12 at 4:56
    
The answer to this question is closely related to your earlier question which I have already answered. –  Metrics Dec 31 '12 at 13:27
add comment

lag = 4 for quarterly, and lag = 12 for monthly data

share|improve this answer
    
Welcome to the site, @craig. It seems to be you're assuming the data are monthly, but that isn't specified in the question. What if the data were 1 value per year, for instance, would you still want lag=4 for quarterly? Since you're new here, it may be helpful for you to read our FAQ, which has lots of into about site policies & how best to answer questions. –  gung Oct 2 '12 at 17:02
add comment

We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.