# What is the correct procedure to choose the lag when performing Johansen cointegration test?

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.

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## 2 Answers

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).

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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
the above information is quite helpful. However, how do we determine appropriate lag length for daily financial data like stock market, commodity prices? –  user45915 May 21 '14 at 11:47

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.

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It should be added that the information criteria should be calculated on VAR model in levels. –  mpiktas Dec 30 '12 at 8:01

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