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Bandwidth Selection, Prewhitening, and the Power of the Phillips-Perron Test

Published online by Cambridge University Press:  11 February 2009

Yin-Wong Cheung  and
Kon S. Lai
Yin-Wong Cheung
Affiliation:
University of California at Santa Cruz and City University of Hong Kong
Kon S. Lai
Affiliation:
California State University at Los Angeles
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Abstract

This study examines several important practical issues concerning nonparametric estimation of the innovation variance for the Phillips-Perron (PP) test. A Monte Carlo study is conducted to evaluate the potential effects of kernel choice, databased bandwidth selection, and prewhitening on the power property of the PP test in finite samples. The Monte Carlo results are instructive. Although the kernel choice is found to make little difference, data-based bandwidth selection and prewhitening can lead to power gains for the PP test. The combined use of both the Andrews (1991, Ecpnometrica 59, 817–858) data-based bandwidth selection procedure and the Andrews and Monahan (1992, Econometrica 60, 953–966) prewhitening procedure performs particularly well. With the combined use of these two procedures, the PPtest displays relatively good power in comparison with the augmented Dickey-Fuller test.

Type
Articles
Information
Econometric Theory , Volume 13 , Issue 5 , October 1997 , pp. 679 - 691
Copyright
Copyright © Cambridge University Press 1997

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References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.Google Scholar
Andrews, D.W.K. & Monahan, J.C. (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953–966.CrossRefGoogle Scholar
Cheung, Y.W. & Lai, K.S. (1995a) Bandwidth selection, prewhitening, and the power of the Phillips-Perron test. Working paper 324, Department of Economics, University of California at Santa Cruz.Google Scholar
Cheung, Y. W. & Lai, K.S. (1995b) Lag order and critical values of the augmented Dickey-Fuller test. Journal of Business and Economic Statistics 13, 277–280.Google Scholar
Cheung, Y.W. & Lai, K.S. (1995c) Lag order and critical values of a modified Dickey-Fuller test. Oxford Bulletin of Economics and Statistics 57, 411–419.CrossRefGoogle Scholar
DeJong, D.N., Nankervis, J.C., Savin, N.E., & Whiteman, C.H. (1992) The power problems of unit-root tests in time series with autoregressive errors. Journal of Econometrics 53, 323–343.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, 427–431.Google Scholar
Hall, A. (1994) Testing for a unit root in time series with pretest data-based model selection. Journal of Business and Economic Statistics 12, 461–470.CrossRefGoogle Scholar
Hannan, E.J. & J. Rissanen (1982) Recursive estimation of ARMA order. Biometrika 69, 81–94.CrossRefGoogle Scholar
Kim, K. & P. Schmidt (1990) Some evidence on the accuracy of Phillips-Perron tests using alternative estimates of nuisance parameters. Economics Letters 34, 345–350.CrossRefGoogle Scholar
Lee, C.C. & P.Phillips, C.B. (1994) An ARMA prewhitened long-run variance estimator. Working paper, Department of Economics, Yale University.Google Scholar
Newey, W.K. & West, K.D. (1987) A simple positive definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.CrossRefGoogle Scholar
Newey, W.K. & (West, K.D. (1994) Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–653.Google Scholar
Ng, S. & P. Perron (1995) Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. Journal of the American Statistical Association 90, 268–281.CrossRefGoogle Scholar
Perron, P. & S. Ng (1995) Useful modifications to some unit root tests with dependent errors and their local asymptotic properties. Working paper, Department de Sciences conomiques et C.R.D.E., University de Montreal.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–301.CrossRefGoogle Scholar
Phillips, P.C.B. & P. Perron (1988) Testing for a unit root in time series regression. Biometrika 75, 335–346.CrossRefGoogle Scholar
Priestley, M.B. (1981) Spectral Analysis and Tune Series. New York: Academic Press.Google Scholar
Robinson, P.M. (1991) Automatic frequency domain inference on semiparametric and nonparametric models. Econometrica 59, 1329–1363.CrossRefGoogle Scholar
Rohatgi, V.K. (1984) Statistical Inference. New York: Wiley.Google Scholar
Schwarz, G. (1978) Estimating the dimension of a model. Annals of Statistics 6, 461–464.CrossRefGoogle Scholar
Schwert, G.W. (1989) Tests for unit roots: A Monte Carlo investigation. Journal of Business and Economic Statistics 7, 147–159.CrossRefGoogle Scholar
Silverman, B.W. (1986) Density Es timation for Statistics and Data Analysis. London: Chapman and Hall.Google Scholar
Stock, J.H. (1994) Unit roots, structural breaks and trends. In Engle, R.R & McFadden, D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2739–2841. New York: North-Holland.Google Scholar