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A GENERALIZED PORTMANTEAU TEST FOR INDEPENDENCE BETWEEN TWO STATIONARY TIME SERIES

Published online by Cambridge University Press:  01 February 2009

Xiaofeng Shao
Xiaofeng Shao*
Affiliation:
University of Illinois at Urbana-Champaign
*
*Address correspondence to Xiaofeng Shao, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright St., Champaign, IL 61820, USA; e-mail: [email protected].
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Abstract

We propose generalized portmanteau-type test statistics in the frequency domain to test independence between two stationary time series. The test statistics are formed analogous to the one in the paper by Chen and Deo (2004, Econometric Theory 20, 382–416), who extended the applicability of the portmanteau goodness-of-fit test to the long memory case. Under the null hypothesis of independence, the asymptotic standard normal distributions of the proposed statistics are derived under fairly mild conditions. In particular, each time series is allowed to possess short memory, long memory, or antipersistence. A simulation study shows that the tests have reasonable size and power properties.

Type
ARTICLES
Information
Econometric Theory , Volume 25 , Issue 1 , February 2009 , pp. 195 - 210
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Beran, J. (1994) Statistic for Long-Memory Processes. Chapman and Hall.Google Scholar
Beran, J., Bhansali, R.J., & Ocker, D. (1998) On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes. Biometrika 85, 921–934.CrossRefGoogle Scholar
Bhansali, R.J., Giraitis, L., & Kokoszka, P.S. (2006) Estimation of the memory parameter by fitting fractionally differenced autoregressive models. Journal of Multivariate Analysis 97, 2101–2130.CrossRefGoogle Scholar
Bouhaddioui, C. & Roy, R. (2006) A generalized portmanteau test for independence of two infinite-order vector autoregressive series. Journal of Time Series Analysis 27, 505–544.CrossRefGoogle Scholar
Box, G. & Pierce, D. (1970) Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association 65, 1509–1526.CrossRefGoogle Scholar
Chen, W. & Deo, R.S. (2004a) A generalized portmanteau goodness-of-fit test for time series models. Econometric Theory 20, 382–416.CrossRefGoogle Scholar
Chen, W. & Deo, R.S. (2004b) Power transformations to induce normality and their applications. Journal of the Royal Statistical Society, Series B. 66, 117–130.CrossRefGoogle Scholar
Dahlhaus, R. (1989) Efficient parameter estimation for self-similar processes. Annals of Statistics 17, 1749–1766.CrossRefGoogle Scholar
Doukhan, P., Oppenheim, G., & Taqqu, M.S. (2003) Theory and Applications of Long-Range Dependence. Birkhaüser.Google Scholar
Duchesne, P. & Roy, R. (2003) Robust tests for independence of two time series. Statistica Sinica 13, 827–852.Google Scholar
Eichler, M. (2007) A frequency-domain based test for non-correlation between stationary time series. Metrika 65, 133–157.CrossRefGoogle Scholar
El Himdi, K. & Roy, R. (1997) Tests for noncorrelation of two multivariate ARMA time series. Canadian Journal of Statistics 25, 233–256.CrossRefGoogle Scholar
Fox, R. & Taqqu, M.S. (1986) Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Annals of Statistics 14, 517–532.CrossRefGoogle Scholar
Giraitis, L. & Surgailis, D. (1990) A central limit theorem for quadratic forms in strongly dependent random variables and its application to asymptotic normality of Whittle’s estimate. Probability Theory and Related Fields 86, 87–104.CrossRefGoogle Scholar
Hallin, M. & Saidi, A. (2005) Testing non-correlation and non-causality between multivariate ARMA time series. Journal of Time Series Analysis 26, 83–106.CrossRefGoogle Scholar
Hallin, M. & Saidi, A. (2007) Optimal tests of non-correlation between multivariate time series. Journal of the American Statistical Association 102, 938–952.CrossRefGoogle Scholar
Hannan, E.J. (1973) The asymptotic theory of linear time series models. Journal of Applied Probability 10, 130–145.CrossRefGoogle Scholar
Haugh, L.D. (1976) Checking the independence of two covariance-stationary time series: A univariate residual cross-correlation approach. Journal of the American Statistical Association 71, 378–385.CrossRefGoogle Scholar
Hong, Y. (1996) Testing for independence between two covariance stationary time series. Biometrika 83, 615–625.CrossRefGoogle Scholar
Ling, S. & Li, W.K. (1997) On fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity. Journal of the American Statistical Association 92, 1184–1194.CrossRefGoogle Scholar
Martin, V.L. & Wilkins, N.P. (1999) Indirect estimation of ARFIMA and VARFIMA models. Journal of Econometrics 93, 149–175.CrossRefGoogle Scholar
Pham, D., Roy, R., & Cédras, L. (2003) Tests for non-correlation of two cointegrated ARMA time series. Journal of Time Series Analysis 24, 553–577.CrossRefGoogle Scholar
Priestley, M.B. (1981) Spectral Analysis and Time Series, vol. 1, Academic Press.Google Scholar
Robinson, P.M. (2003) Time Series with Long Memory. Oxford University Press.CrossRefGoogle Scholar
Shao, X. (2007) A Generalized Portmanteau Test for Independence between Two Stationary Time Series. Technical Report, Department of Statistics, University of Illinois at Urbana-Champaign.Google Scholar
Teyssière, G. & Kirman, A. (2005) Long Memory in Economics. Springer-Verlag.Google Scholar
Velasco, C. & Robinson, P.M. (2000) Whittle pseudo-maximum likelihood estimation for nonstationary time series. Journal of the American Statistical Association 95, 1229–1243.CrossRefGoogle Scholar