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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 4 (1988)
Issue (Month): 03 (December)
Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_ECTProvider-Email:email@example.com
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 &bull Diffusion Processes
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.:
- 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.
- 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.
- 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.
- West, Kenneth D, 1988. "Asymptotic Normality, When Regressors Have a Unit Root," Econometrica, Econometric Society, vol. 56(6), pages 1397-1417, November.
- 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.
- 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.
- Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
- 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.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- 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.
- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
- 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.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.