Statistical Inference in Regressions with Integrated Processes: Part 1
AbstractThis 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.
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Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 4 (1988)
Issue (Month): 03 (December)
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Other versions of this item:
- Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
- 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.
- 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.
- 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.
- Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 473-95, August.
- Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
- West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
- 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.
- Peter C.B. Phillips & Pierre Perron, 1986.
"Testing for a Unit Root in Time Series Regression,"
Cowles Foundation Discussion Papers
795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
- 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.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
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