Probability Properties of <i>I</i> (1) Processes

Søren Johansen

in Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Published in print December 1995 | ISBN: 9780198774501
Published online November 2003 | e-ISBN: 9780191596476 | DOI:

Series: Advanced Texts in Econometrics

 							Probability Properties of I (1) Processes

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The basic properties of I(1) processes defined by the vector autoregressive model with a constant term are given. We discuss the behaviour of the process in different directions, and apply these results to find asymptotic properties of various product moment matrices needed to derive properties of likelihood ratio tests and estimators. Estimators and test statistics are derived under the assumption of Gaussian errors, but the limit results are proved under the more general assumption that the errors are independent with the same distribution with mean zero and finite variance.

Keywords: asymptotic properties; Gaussian errors; I(1) process; product moment

Chapter.  4809 words. 

Subjects: Econometrics and Mathematical Economics

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