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Likelihood-Based Inference in Cointegrated Vector Autoregressive Models$
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Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Søren Johansen

Print publication date: 1995

Print ISBN-13: 9780198774501

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774508.001.0001

Probability Properties of I (1) Processes

Chapter:
(p. 141 ) 10 Probability Properties of I (1) Processes
Source:
Likelihood-Based Inference in Cointegrated Vector Autoregressive Models
Author(s):

Søren Johansen (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198774508.003.0010

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

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