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ON AUGMENTED HEGY TESTS FOR SEASONAL UNIT ROOTS

Published online by Cambridge University Press:  27 April 2012

Tomás del Barrio Castro,
Denise R. Osborn and
A.M. Robert Taylor
Tomás del Barrio Castro
Affiliation:
University of the Balearic Islands
Denise R. Osborn
Affiliation:
University of Manchester
A.M. Robert Taylor*
Affiliation:
University of Nottingham
*
*Address correspondence to A.M. Robert Taylor, School of Economics, University of Nottingham NG7 2RD, United Kingdom; e-mail: Robert.Taylor@nottingham.ac.uk.
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Abstract

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In this paper we extend the large-sample results provided for the augmented Dickey–Fuller test by Said and Dickey (1984, Biometrika 71, 599–607) and Chang and Park (2002, Econometric Reviews 21, 431–447) to the case of the augmented seasonal unit root tests of Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238), inter alia. Our analysis is performed under the same conditions on the innovations as in Chang and Park (2002), thereby allowing for general linear processes driven by (possibly conditionally heteroskedastic) martingale difference innovations. We show that the limiting null distributions of the t-statistics for unit roots at the zero and Nyquist frequencies and joint F-type statistics are pivotal, whereas those of the t-statistics at the harmonic seasonal frequencies depend on nuisance parameters that derive from the lag parameters characterizing the linear process. Moreover, the rates on the lag truncation required for these results to hold are shown to coincide with the corresponding rates given in Chang and Park (2002); in particular, an o(T1/2) rate is shown to be sufficient.

Information

Type
Miscellanea
Information
Econometric Theory , Volume 28 , Issue 5 , October 2012, pp. 1121 - 1143
Copyright
Copyright © Cambridge University Press 2012

References

REFERENCES

Beaulieu, J.J. & Miron, J.A. (1993) Seasonal unit roots in aggregate U.S. data. Journal of Econometrics 55, 305–328.Google Scholar
Berk, K.N. (1974) Consistent autoregressive spectral estimates. Annals of Statistics 2, 389–502.Google Scholar
Boswijk, H.P. & Franses, P.H. (1996) Unit roots in periodic autoregressions. Journal of Time Series Analysis 17, 221–245.Google Scholar
Box, G.E.P. & Jenkins, G.M. (1976) Time Series Analysis: Forecasting and Control, rev. ed. Holden-Day.Google Scholar
Burridge, P. & Taylor, A.M.R. (2001) On the properties of regression-based tests for seasonal unit roots in the presence of higher-order serial correlation. Journal of Business & Economic Statistics 3, 374–379.Google Scholar
Chang, Y. & Park, J.Y. (2002) On the asymptotics of ADF tests for unit roots. Econometric Reviews 21, 431–447.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.Google Scholar
Davis, P.J. (1979) Circulant Matrices. Wiley-Interscience.Google Scholar
del Barrio Castro, T. & Osborn, D.R. (2011) HEGY tests in the presence of moving averages. Oxford Bulletin of Economic and Statistics 73, 691–704.Google Scholar
del Barrio Castro, T., Osborn, D.R., & Taylor, A.M.R. (2011) On Augmented HEGY Tests for Seasonal Unit Roots. Working paper 11/02, Granger Centre for Time Series Econometrics.Google Scholar
Fuller, W.A. (1996) Introduction to Statistical Time Series, 2nd ed.Wiley.Google Scholar
Ghysels, E., Lee, H.S., & Noh, J. (1994) Testing for unit roots in seasonal time series: Some theoretical extensions and a Monte Carlo investigation. Journal of Econometrics 62, 415–442.Google Scholar
Ghysels, E. & Osborn, D.R. (2001) The Econometric Analysis of Seasonal Time Series. Cambridge University Press.Google Scholar
Gray, R.M. (2006) Toeplitz and Circulant Matrices, A Review. Foundation and Trends® in Communications and Information Theory. Now Publishers.Google Scholar
Hall, A.R. (1994) Testing for a unit root in time series with pretest data-based model selection. Journal of Business & Economic Statistics 12, 461–470.Google Scholar
Hylleberg, S., Engle, R.F., Granger, C.W.J., & Yoo, B.S. (1990) Seasonal integration and cointegration. Journal of Econometrics 44, 215–238.Google Scholar
Ng, S. & Perron, P. (1995) Unit root tests in ARMA models with data dependent methods for selection of the truncation lag. Journal of the American Statistical Association 90, 268–281.Google Scholar
Ng, S. & Perron, P. (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554.Google Scholar
Osborn, D.R. & Rodrigues, P.M.M. (2002) Asymptotic distributions of seasonal unit root tests: A unifying approach. Econometric Reviews 21, 221–241.CrossRefGoogle Scholar
Phillips, P.C.B. & Durlauf, S.N. (1986) Multiple time series regression with integrated processes. Review of Economic Studies 53, 473–495.Google Scholar
Rodrigues, P.M.M. & Taylor, A.M.R. (2004a) Alternative estimators and unit root tests for seasonal autoregressive processes. Journal of Econometrics 120, 35–73.Google Scholar
Rodrigues, P.M.M. & Taylor, A.M.R. (2004b) Asymptotic distributions for regression-based seasonal unit root test statistics in a near-integrated model. Econometric Theory 20, 645–670.Google Scholar
Rodrigues, P.M.M. & Taylor, A.M.R. (2007) Efficient tests of the seasonal unit root hypothesis. Journal of Econometrics 141, 548–573.Google Scholar
Said, S.E. & Dickey, D.A. (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71, 599–607.CrossRefGoogle Scholar
Smith, R.J. & Taylor, A.M.R. (1998) Additional critical values and asymptotic representations for seasonal unit root tests. Journal of Econometrics 85, 269–288.CrossRefGoogle Scholar
Smith, R.J. & Taylor, A.M.R. (1999) Likelihood ratio tests for seasonal unit roots. Journal of Time Series Analysis 20, 453–476.CrossRefGoogle Scholar
Smith, R.J., Taylor, A.M.R. & del Barrio Castro, T. (2009) Regression-based seasonal unit root tests. Econometric Theory 25, 527–560.Google Scholar
Taylor, A.M.R. (2005) Variance ratio tests of the seasonal unit root hypothesis. Journal of Econometrics 124, 33–54.CrossRefGoogle Scholar