Numerical aspects of a likelihood ratio test statistic for cointegrating rank
This paper concerns numerical aspects of the distributions for the likelihood ratio test statistics for cointegrating rank. These statistics, the trace and the lambda max, play a central part in the maximum likelihood approach to multivariate cointegrating analysis. Their limit distributions are of unit root, or Dickey-Fuller type, and can be represented by functionals of Brownian motions. As of yet, one must in practice rely on simulated critical values. In this paper we investigate how the sample size and the number of replications in the simulations affect the critical values obtained. Moreover, a numerical Markov chain method for obtaining critical values in the univariate case is suggested. Results from the two approaches are compared. Finally, we present new tables of critical values based on a greater number of replications than presently is available.
likelihood ratio test cointegration simulation numerical method