We consider the cointegration tests of Johansen (1988, Journal of Economic Dynamics and
Control 12, 231–254; 1991, Econometrica 59,
1551–1580) when a vector autoregressive (VAR) process of order
k is used to approximate a more general linear process with a
possibly infinite VAR representation. Traditional methods to select the
lag order, such as Akaike's information criterion (AIC) or the
Bayesian information criterion, often lead to too parsimonious a model
with the implication that the cointegration tests suffer from substantial
size distortions in finite samples. We extend the analysis of Ng and
Perron (2001, Econometrica 69,
1519–1554) to derive a modified Akaike's information criterion
(MAIC) in this multivariate setting. The idea is to use the information
specified by the null hypothesis as it relates to restrictions on the
parameters of the model to keep an extra term in the penalty function of
the AIC. This MAIC takes a very simple form for which this extra term is
simply the likelihood ratio test for testing the null hypothesis of
r against more than r cointegrating vectors. We provide
theoretical analyses of its validity and of the fact that cointegration
tests constructed from a VAR whose lag order is selected using the MAIC
have the same limit distribution as when the order is finite and known. We
also provide theoretical and simulation analyses to show how the MAIC
leads to VAR approximations that yield tests with drastically improved
size properties with little loss of power.We are grateful to two referees for especially useful and
constructive comments.