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Oxford Bulletin of Economics and Statistics

Опубликовано на портале: 25-06-2004
Michael Osterwald-Lenum Oxford Bulletin of Economics and Statistics. 1992.  Vol. 54. No. 3. P. 461-472. 
The recent literature on maximum likelihood cointegration theory studies Gaussian vector autoregression (VAR) models allowing for some deterministic components in the form of polynomials in time. An examination is presented of such models for variables integrated at most of order one, when tests for cointegration involve statistics with non-standard asymptotic distributions. The asymptotic distributions of these test statistics are known to be functions of the distribution of certain matrices of stochastic variables involving integrals of Brownian motions. In fact, conditional on which restrictions on the coefficients of the polynomial in time are valid, different asymptotic distributions are obtained. The cases examined exhaust the hypotheses relevant to the cointegration rank analysis of I(1) variables in models involving up to linear trends and possibly seasonal dummies. The examination solves the numerical problem in making most of the interesting quantiles of these asymptotic distributions available to the applied econometrician.