Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown
The distribution of statistics testing restrictions on the coefficients in time series regressions can depend on the order of integration of the regressors. In practice, the order of integration is rarely known. We examine two conventional approaches to this problem — simply to ignore unit root problems or to use unit root pretests to determine the critical values for second-stage inference—and show that both exhibit substantial size distortions in empirically plausible situations. We then propose an alternative approach in which the second-stage critical values depend continuously on a first-stage statistic that is informative about the order of integration of the regressor. This procedure has the correct size asymptotically and good local asymptotic power.
Volume (Year): 10 (1994)
Issue (Month): 3-4 (August)
|Contact details of provider:|| Postal: Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK|
Web page: http://journals.cambridge.org/jid_ECT
References listed on IDEAS
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.:
- Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
- John Y. Campbell, 1990.
"A Variance Decomposition for Stock Returns,"
NBER Working Papers
3246, National Bureau of Economic Research, Inc.
- Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January.
- James H. Stock & Kenneth D. West, 1987.
"Integrated Regressors and Tests of the Permanent Income Hypothesis,"
NBER Working Papers
2359, National Bureau of Economic Research, Inc.
- Stock, James H. & West, Kenneth D., 1988. "Integrated regressors and tests of the permanent-income hypothesis," Journal of Monetary Economics, Elsevier, vol. 21(1), pages 85-95, January.
- Flavin, Marjorie A, 1981. "The Adjustment of Consumption to Changing Expectations about Future Income," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 974-1009, October.
- Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991.
"Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?,"
Cowles Foundation Discussion Papers
979, Cowles Foundation for Research in Economics, Yale University.
- Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
- Tom Doan, . "KPSS: RATS procedure to perform KPSS (Kwiatowski, Phillips, Schmidt, and Shin) stationarity test," Statistical Software Components RTS00100, Boston College Department of Economics.
- Phillips, P C B, 1991.
"Optimal Inference in Cointegrated Systems,"
Econometric Society, vol. 59(2), pages 283-306, March.
- Tanaka, Katsuto, 1990. "Testing for a Moving Average Unit Root," Econometric Theory, Cambridge University Press, vol. 6(04), pages 433-444, December.
- Perron, P., 1991. "A Test for Changes in a Polynomial Trend Functions for a Dynamioc Time Series," Papers 363, Princeton, Department of Economics - Econometric Research Program.
- Park, Joon Y. & Phillips, Peter C.B., 1989.
"Statistical Inference in Regressions with Integrated Processes: Part 2,"
Cambridge University Press, vol. 5(01), pages 95-131, April.
- Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
- Gregory Mankiw, N. & Shapiro, Matthew D., 1985.
"Trends, random walks, and tests of the permanent income hypothesis,"
Journal of Monetary Economics,
Elsevier, vol. 16(2), pages 165-174, September.
- Matthew D. Shapiro & N. Gregory Mankiw, 1984. "Trends, Random Walks, and Tests of the Permanent Income Hypothesis," Cowles Foundation Discussion Papers 725, Cowles Foundation for Research in Economics, Yale University.
- Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality: A Theoretical Overview and Simulation Study," Cowles Foundation Discussion Papers 1001, Cowles Foundation for Research in Economics, Yale University.
- Fama, Eugene F. & French, Kenneth R., 1989. "Business conditions and expected returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 25(1), pages 23-49, November.
- Nabeya, Seiji & Tanaka, Katsuto, 1990. "A General Approach to the Limiting Distribution for Estimators in Time Series Regression with Nonstable Autoregressive Errors," Econometrica, Econometric Society, vol. 58(1), pages 145-63, January.
- Peter C.B. Phillips, 1988. "Spectral Regression for Cointegrated Time Series," Cowles Foundation Discussion Papers 872, Cowles Foundation for Research in Economics, Yale University.
- Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(01), pages 1-21, March.
When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:10:y:1994:i:3-4:p:672-700_00. See general 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.