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A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics

A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank... Michael Osterwald-Lenurn? I. INTRODUCTION The recent literature on maximum likelihood cointegration theory studies Gaussian VAR models allowing for some deterministic components in the form of polynomials in time. Here we are concerned with such models for variables integrated at most of order one, when tests for cointegration involve statistics with non-standard asymptotic distributions. Cf. Johansen ( 1988), (1991a), (1991b), Johansen and Juselius (1990). The asymptotic distributions o these test statistics are known to be functions of the distribution of certain f 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 dealt with here .exhaust the hypotheses relevant to the cointegration rank analysis of I( 1)variables in models involving up to linear trends and possibly seasonal dummies. This paper solves the numerical problem in making most of the interesting quantiles of these asymptotic distributions available to the applied econometrician. It thus includes recalculated and extended versions of the four tables presented in Johansen (1988) and Johansen and Juselius (1990)as well as two new tables. 'This note was written during a visit 1 July 1989-1 June 1990 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Oxford Bulletin of Economics & Statistics Wiley

A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics

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References (4)

Publisher
Wiley
Copyright
1992 Blackwell Publishers Ltd
ISSN
0305-9049
eISSN
1468-0084
DOI
10.1111/j.1468-0084.1992.tb00013.x
Publisher site
See Article on Publisher Site

Abstract

Michael Osterwald-Lenurn? I. INTRODUCTION The recent literature on maximum likelihood cointegration theory studies Gaussian VAR models allowing for some deterministic components in the form of polynomials in time. Here we are concerned with such models for variables integrated at most of order one, when tests for cointegration involve statistics with non-standard asymptotic distributions. Cf. Johansen ( 1988), (1991a), (1991b), Johansen and Juselius (1990). The asymptotic distributions o these test statistics are known to be functions of the distribution of certain f 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 dealt with here .exhaust the hypotheses relevant to the cointegration rank analysis of I( 1)variables in models involving up to linear trends and possibly seasonal dummies. This paper solves the numerical problem in making most of the interesting quantiles of these asymptotic distributions available to the applied econometrician. It thus includes recalculated and extended versions of the four tables presented in Johansen (1988) and Johansen and Juselius (1990)as well as two new tables. 'This note was written during a visit 1 July 1989-1 June 1990

Journal

Oxford Bulletin of Economics & Statistics – Wiley

Published: Aug 1, 1992

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