Hostname: page-component-89b8bd64d-7zcd7 Total loading time: 0 Render date: 2026-05-10T00:50:36.920Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE ALTERNATIVE LONG-RUN VARIANCE RATIO TEST FOR A UNIT ROOT

Published online by Cambridge University Press:  15 March 2006

Ye Cai  and
Mototsugu Shintani
Ye Cai
Affiliation:
Vanderbilt University
Mototsugu Shintani
Affiliation:
Vanderbilt University
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper investigates the effects of consistent and inconsistent long-run variance estimation on a test for a unit root, based on the generalization of the von Neumann ratio. The results from the Monte Carlo experiments suggest that the unit root tests based on an inconsistent estimator have less size distortion and more stability of size across different autocorrelation specifications as compared to the tests based on a consistent estimator. This improvement in size property, however, comes at the cost of a loss in power. The finite-sample power, in addition to the local asymptotic power, of the tests with an inconsistent estimator is shown to be much lower than that of conventional tests. This finding can be well generalized to the test for cointegration in a multivariate system. The paper also points out that combining consistent and inconsistent estimators in the long-run variance ratio test is one possibility of balancing the size and power.The authors thank two anonymous referees, Pentti Saikkonen, and participants of the 2004 Midwest Econometrics Group meetings, 2005 Spring Meetings of The Japanese Economic Association, and a workshop at Vanderbilt University for helpful comments and suggestions.

Information

Type
Research Article
Information
Econometric Theory , Volume 22 , Issue 3 , June 2006 , pp. 347 - 372
Copyright
© 2006 Cambridge University Press

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.CrossRefGoogle Scholar
Berk, K.N. (1974) Consistent autoregressive spectral estimates. Annals of Statistics 2, 489–502.CrossRefGoogle Scholar
Bhargava, A. (1986) On the theory of testing for unit roots in observed time series. Review of Economic Studies 53, 369–384.CrossRefGoogle Scholar
Breitung, J. (2002) Nonparametric tests for unit roots and cointegration. Journal of Econometrics 108, 343–363.CrossRefGoogle Scholar
Elliott, G., T. Rothenberg, & J.H. Stock (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813–836.CrossRefGoogle Scholar
Harris, D. & D.S. Poskitt (2004) Determination of cointegrating rank in partially non-stationary processes via a generalised von-Neumann criterion. Econometrics Journal 7, 191–217.CrossRefGoogle Scholar
Jansson, M. (2004) The error in rejection probability of simple autocorrelation robust tests. Econometrica 72, 937–946.CrossRefGoogle Scholar
Kiefer, N.M. & T.J. Vogelsang (2002) Heteroskedasticity-autocorrelation robust standard errors using the Bartlett kernel without truncation. Econometrica 70, 2093–2095.CrossRefGoogle Scholar
Kiefer, N.M., T.J. Vogelsang, & H. Bunzel (2000) Simple robust testing of regression hypotheses. Econometrica 68, 695–714.CrossRefGoogle Scholar
Müller, U.K. (2005) Size and power of tests of stationarity in highly autocorrelated time series. Journal of Econometrics 128, 195–213.CrossRefGoogle Scholar
Nabeya, S. & K. Tanaka (1990) Limiting power of unit-root tests in time-series regression. Journal of Econometrics 46, 247–271.CrossRefGoogle Scholar
Newey, W.K. & K.D. West (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708.CrossRefGoogle Scholar
Park, J.Y. & P.C.B. Phillips (1988) Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4, 468–497.CrossRefGoogle Scholar
Park, J.Y. & P.C.B. Phillips (1989) Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5, 95–131.CrossRefGoogle Scholar
Perron, P. & S. Ng (1996) Useful modifications to unit root tests with dependent errors and their local asymptotic properties. Review of Economic Studies 63, 435–464.CrossRefGoogle Scholar
Phillips, P.C.B. (1987) Time series regression with a unit root. Econometrica 55, 277–301.CrossRefGoogle Scholar
Phillips, P.C.B. & S. Ouliaris (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165–193.CrossRefGoogle Scholar
Phillips, P.C.B. & P. Perron (1988) Testing for a unit root in time series regression. Biometrika 75, 335–346.CrossRefGoogle Scholar
Phillips, P.C.B. & Z. Xiao (1998) A primer on unit root testing. Journal of Economic Surveys 12, 423–469.CrossRefGoogle Scholar
Sargan, J.D. & A. Bhargava (1983) Testing residuals from least squares regression for being generated by the Gaussian random walk. Econometrica 51, 153–174.CrossRefGoogle Scholar
Schmidt, P. & P.C.B. Phillips (1992) LM tests for a unit root in the presence of deterministic trends. Oxford Bulletin of Economics and Statistics 54, 257–287.CrossRefGoogle Scholar
Schwert, G.W. (1989) Tests for unit roots: A Monte Carlo investigation. Journal of Business & Economic Statistics 7, 147–159.Google Scholar
Shintani, M. (2001) A simple cointergrating rank test without vector autoregression. Journal of Econometrics 105, 337–362.CrossRefGoogle Scholar
Stock, J.H. (1994) Unit roots, structural breaks and trends. In R.F. Engle & D. McFadden (eds.), Handbook of Econometrics, vol. 4, pp. 2740–2841. North-Holland.
Stock, J.H. (1999) A class of tests for integration and cointegration. In R.F. Engle & H. White (eds.), Cointegration, Causality and Forecasting: A Festschrift for Clive W.J. Granger, pp. 135–167. Oxford University Press.