Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-14T23:06:51.744Z Has data issue: false hasContentIssue false
  • English
  • Français

Inference in Models with Nearly Integrated Regressors

Published online by Cambridge University Press:  11 February 2009

Christopher L. Cavanagh ,
Graham Elliott  and
James H. Stock
Christopher L. Cavanagh
Affiliation:
Columbia University
Graham Elliott
Affiliation:
University of California, San Diego
James H. Stock
Affiliation:
Kennedy School of Government Harvard University and National Bureau of Economic Research
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper examines regression tests of whether x forecasts y when the largest autoregressive root of the regressor is unknown. It is shown that previously proposed two-step procedures, with first stages that consistently classify x as I(1) or I(0), exhibit large size distortions when regressors have local-to-unit roots, because of asymptotic dependence on a nuisance parameter that cannot be estimated consistently. Several alternative procedures, based on Bonferroni and Scheffe methods, are therefore proposed and investigated. For many parameter values, the power loss from using these conservative tests is small.

Type
Articles
Information
Econometric Theory , Volume 11 , Issue 5 , October 1995 , pp. 1131 - 1147
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bobkoski, M.J. (1983) Hypothesis Testing in Nonstationary Time Series. Unpublished Ph.D. Thesis, University of Wisconsin.Google Scholar
Campbell, J.Y. & Shiller, R.J. (1988) Stock prices, earnings and expected dividends. Journal of Finance 43, 661–676.CrossRefGoogle Scholar
Cavanagh, C. (1985) Roots Local to Unity. Manuscript, Harvard University.Google Scholar
Chan, N.H. (1988) On the parameter inference for nearly nonstationary time series. Journal of the American Statistical Association 83 (403), 857–862.CrossRefGoogle Scholar
Chan, N.H. & Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR(1) processes. Annals of Statistics 15, 1050–1063.CrossRefGoogle Scholar
Dickey, D.A. & Fuller, W.A. (1979) Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74 (366), 427–431.Google Scholar
Dufour, J.M. (1990) Exact tests and confidence sets in linear regression with autocorrelated errors. Econometrica 58, 475–494.CrossRefGoogle Scholar
Elliott, G. (1994) Application of Local to Unity Asymptotic Theory to Time Series Regression. Ph.D. Dissertation, Harvard University.Google Scholar
Elliott, G. & Stock, J.H. (1994) Inference in time series regression when the order of integration of a regressor is unknown. Econometric Theory 10, 672–700.CrossRefGoogle Scholar
Fama, E.F. (1991) Efficient capital markets II. Journal of Finance 46 (5), 1575–1617.CrossRefGoogle Scholar
Kitamura, Y. & Phillips, P.C.B. (1992) Fully Modified IV, GIVE, and GMM Estimation with Possibly Nonstationary Regressors and Instruments. Manuscript, Cowles Foundation, Yale University.Google Scholar
Lehmann, E.L. (1959) Testing Statistical Hypotheses. New York: Wiley.Google Scholar
Nabeya, S. & Sørensen, B.E. (1994) Asymptotic distributions of the least-squares estimators and test statistics in the near unit root model with non-zero initial value and local drift and trend. Econometric Theory 10, 937–966.CrossRefGoogle Scholar
Pantula, S.G. (1991) Asymptotic distributions of the unit-root tests when the process is nearly stationary. Journal of Business and Economic Statistics 9, 63–71.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1988) Statistical inference in regressions with integrated processes: Part I. Econometric Theory 4, 468–497.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Toward a unified asymptotic theory for autoregression. Biometrika 74, 535–547.CrossRefGoogle Scholar
Phillips, P.C.B. (1995) Fully modified least squares and vector autoregression. Econometrica 63, 1023–1078.CrossRefGoogle Scholar
Phillips, P.C.B. & Ploberger, W. (1991) Time Series Modeling with a Bayesian Frame of Reference: I. Concepts and Illustrations. Manuscript, Cowles Foundation, Yale University.Google Scholar
Sims, C.A., Stock, J.H., & Watson, M.W. (1990) Inference in Linear Time Series Models with Some Unit Roots. Econometrica 58, 113–144.CrossRefGoogle Scholar
Stock, J.H. (1991) Confidence intervals for the largest autoregressive root in U.S. economic time series. Journal of Monetary Economics 28 (3), 435–460.CrossRefGoogle Scholar
Stock, J.H. (1994) Deciding between I(0) and I(1). Journal of Econometrics 63, 105–131.CrossRefGoogle Scholar