Statistical Inference in Regressions with Integrated Processes: Part 1
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.
|Date of creation:||1986|
|Date of revision:||Aug 1987|
|Publication status:||Published in Econometric Theory (1988), 4: 468-497|
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- Phillips, P.C.B., 1986.
"Testing for a Unit Root in Time Series Regression,"
Cahiers de recherche
8633, Universite de Montreal, Departement de sciences economiques.
- P. C. B. Phillips & S. N. Durlauf, 1986.
"Multiple Time Series Regression with Integrated Processes,"
Review of Economic Studies,
Oxford University Press, vol. 53(4), pages 473-495.
- Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
- Peter C.B. Phillips & Joon Y. Park, 1986. "Asymptotic Equivalence of OLS and GLS in Regressions with Integrated Regressors," Cowles Foundation Discussion Papers 802, Cowles Foundation for Research in Economics, Yale University.
- Engle, Robert F & Granger, Clive W J, 1987.
"Co-integration and Error Correction: Representation, Estimation, and Testing,"
Econometric Society, vol. 55(2), pages 251-76, March.
- Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Andrews, Donald W. K., 1987. "Least Squares Regression with Integrated or Dynamic Regressors under Weak Error Assumptions," Econometric Theory, Cambridge University Press, vol. 3(01), pages 98-116, February.
- Durlauf, Steven N & Phillips, Peter C B, 1988.
"Trends versus Random Walks in Time Series Analysis,"
Econometric Society, vol. 56(6), pages 1333-54, November.
- Steven N. Durlauf & Peter C.B. Phillips, 1986. "Trends Versus Random Walks in Time Series Analysis," Cowles Foundation Discussion Papers 788, Cowles Foundation for Research in Economics, Yale University.
- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
- West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
- Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
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