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TESTING FOR LONG MEMORY

Published online by Cambridge University Press:  06 September 2007

David Harris ,
Brendan McCabe  and
Stephen Leybourne
David Harris
Affiliation:
University of Melbourne
Brendan McCabe
Affiliation:
University of Liverpool
Stephen Leybourne
Affiliation:
University of Nottingham
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Abstract

This paper introduces a new test statistic for the null hypothesis of short memory against long memory alternatives. The novelty of our statistic is that it is based on only high-order sample autocovariances and by construction eliminates the effects of nuisance parameters typically induced by short memory autocorrelation. For practically relevant situations where the short memory process is not directly observed, but instead appears as the disturbance term in a deterministic linear regression model, we are able to demonstrate that our residual-based statistic has an asymptotic standard normal distribution under the null hypothesis. We also establish consistency of the statistic under long memory alternatives. The finite-sample properties of our procedure are compared to other well-known tests in the literature via Monte Carlo simulations. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.We thank the associate editor and two anonymous referees for their valuable comments on an earlier draft of this paper.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 1 , February 2008 , pp. 143 - 175
Copyright
© 2008 Cambridge University Press

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References

REFERENCES

Brockwell, P.J. & R. Davis (1991) Time Series: Theory and Methods. Springer-Verlag.
Delgado, M.A. & P.M. Robinson (1996) Optimal spectral bandwidth for long memory. Statistica Sinica 6, 97–112.Google Scholar
Hannan, E.J. (1970) Multiple Time Series. Wiley.
Hobijn, B., P.H. Franses, & M. Ooms (2004) Generalizations of the KPSS-test for stationarity. Statistica Neerlandica 58, 483–502.Google Scholar
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, & Y. Shin (1992) Testing the null of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics 54, 159–178.Google Scholar
Lee, D. & P. Schmidt (1996) On the power of the KPSS test of stationarity against fractionally-integrated alternatives. Journal of Econometrics 73, 285–302.Google Scholar
Lobato, I.N. & P.M. Robinson (1998) A nonparametric test for I(0). Review of Economic Studies 65, 475–495.Google Scholar
Newey, W.K. & K.D. West (1994) Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–653.Google Scholar
Robinson, P.M. (1994) Efficient tests of nonstationary hypotheses. Journal of the American Statistical Association 89, 1420–1437.Google Scholar
Sul, D., P.C.B. Phillips, & C.-Y. Choi (2005) Prewhitening bias in HAC estimation. Oxford Bulletin of Economics and Statistics 67, 517–546.Google Scholar
Tanaka, K. (1999) The nonstationary fractional unit root. Econometric Theory 15, 549–582.Google Scholar