I am trying to use urca library to do cointegration test, and its function ca.jo, which conducts the Johansen procedure on a given data set.

I think a lag order of 1 is possible for a cointegrated VECM, which means it does not have short term error correction. For example, we have VAR(1)

$$

X_t=Pi_1X_{t-1} + epsilon_t

$$

and its VECM is

$$

Delta X_t = Pi X_{t-1} + epsilon_t

$$

where $Pi=Pi_1-I_2$

Why does ca.jo specify the minimum lag order to be 2? Is there a reason behind it?

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#### Best Answer

I updated the package *tsDyn* (version 0.9-40 submitted to CRAN), so that its *VECM()* function can handle your case of lag=1. Note that:

- With function
*VECM()*, use lag=0 for the case you described as lag=1 - A warning will be printed, as
*fevd()*,*irf()*,*predict()*et al are not guaranteed to work - If you want no intercept, use:
*include="none"*

Example:

`library(tsDyn) data(barry) summary(VECM(barry, lag=0, estim="ML")) ############# ###Model VECM ############# Full sample size: 324 End sample size: 323 Number of variables: 3 Number of estimated slope parameters 6 AIC -4871.5 BIC -4848.83 SSR 29.3275 Cointegrating vector (estimated by ML): dolcan cpiUSA cpiCAN r1 1 -0.021234 0.0402079 ECT Intercept Equation dolcan -0.0004(0.0011) 0.0024(0.0030) Equation cpiUSA -0.0436(0.0155)** 0.3685(0.0413)*** Equation cpiCAN -0.0824(0.0214)*** 0.4649(0.0572)*** `

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