Abstract
The aim of this paper is to present robust individual tests in autoregressive models with exogenous variables. We derive the asymptotic distribution of the RA-ARX estimators introduced in Duchesne (2004a), following an approach similar to Bustos and Yohai (1986). In particular, we give the asymptotic covariance structure of the RA-ARX estimators. Using this result, we establish the asymptotic distribution of the robustified residual autocorrelations under the null hypothesis of adequacy, which is normal. Some simulation results are reported.
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References
Bustos, O.H. and Yohai, V.J. (1986). Robust estimates for ARMA processes. Journal of the American Statistical Association, 81:155–168.
Denby, L. and Martin, R.D. (1979). Robust estimation of the first-order autoregressive parameter. Journal of the American Statistical Association, 74:140–146.
Duchesne, P. (2004a). Robust and powerful serial correlation tests with new robust estimates in ARX models. Forthcoming in Journal of Time Series Analysis.
Duchesne, P. (2004b). On the asymptotic distribution of residual autocovariances in VARX models with applications. Forthcoming in Test.
Durrett, R. (1995). Probability, Theory and Examples. Second Ed, Duxbury Press, Belmont, CA.
Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A. (1986). Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.
Li, W.K. (1988). A goodness-of-fit test in robust time series modelling. Biometrika, 75:355–361.
Li, W.K. (2004). Diagnostic Checks in Time Series. Chapman & Hall/CRC, New York.
Martin, R.D. and Yohai, V.J. (1985). Robustness in time series and estimating ARMA models. In: E.J. Hannan, P.J. Krishnaiah, and M.M. Rao (eds.), Handbook of Statistics 5:119–155, Elsevier, Amsterdam.
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Bou-Hamad, I., Duchesne, P. (2005). On Robust Diagnostics at Individual Lags Using RA-ARX Estimators. In: Duchesne, P., RÉMillard, B. (eds) Statistical Modeling and Analysis for Complex Data Problems. Springer, Boston, MA. https://doi.org/10.1007/0-387-24555-3_7
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DOI: https://doi.org/10.1007/0-387-24555-3_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24554-6
Online ISBN: 978-0-387-24555-3
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