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Statistical Inference in Regressions with Integrated Processes: Part 1

Published online by Cambridge University Press:  18 October 2010

Joon Y. Park  and
Peter C.B. Phillips
Joon Y. Park
Affiliation:
Cowles Foundation, Yale University
Peter C.B. Phillips
Affiliation:
Cowles Foundation, Yale University
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Abstract

This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions, and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F tests is explored and new transformations are introduced to deal with these dependencies. Some specializations of our theory are considered in detail. In models with strictly exogenous regressors, we demonstrate the validity of conventional asymptotic theory for appropriately constructed Wald tests. These tests provide a simple and convenient basis for specification robust inferences in this context. Single equation regression tests are also studied in detail. Here it is shown that the asymptotic distribution of the Wald test is a mixture of the chi square of conventional regression theory and the standard unit-root theory. The new result accommodates both extremes and intermediate cases.

Type
Research Article
Information
Econometric Theory , Volume 4 , Issue 3 , December 1988 , pp. 468 - 497
Copyright
Copyright © Cambridge University Press 1988 

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