On the non-existence of a Bartlett correction for unit root tests

✍ Scribed by J.L. Jensen; Andrew T.A. Wood

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 358 KB
• Volume: 35
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(97)00012-6

✦ Synopsis

There has been considerable recent interest in testing for a unit root in autoregressive models, especially in the context of cointegration models in econometrics. The likelihood ratio test for a unit root has non-standard asymptotic behaviour. In particular, when the errors are Gaussian, the limiting null distribution of the likelihood ratio statistic, W, is a certain functional of Brownian motion, rather than chi-squared. Moreover, numerical work has shown that the limiting distribution of W is not always a good approximation to the actual distribution. Consequently, there is a need for improved distributional approximations, and the question of whether W admits a Bartlett correction is of interest. In this note we establish that a Bartlett correction does not exist in the simplest unit root model. (~) 1997 Elsevier Science B.V.