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Estimation of the index parameter for autoregressive data using the estimated innovations

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  • Allen, Michael R.
  • Datta, Somnath

Abstract

In this paper we consider an invertible autoregressive process where the innovations (errors) are i.i.d. satisfying a tail regularity condition. The problem of estimation of the index of regular variation [alpha] based on a finite realization of the time series is addressed. We propose the use of a recently developed estimator of [alpha] with the data values replaced by residuals obtained from the model. Consistency and asymptotic normality of the resulting estimator are established and its performance is compared with the original estimator calculated at the data values.

Suggested Citation

  • Allen, Michael R. & Datta, Somnath, 1999. "Estimation of the index parameter for autoregressive data using the estimated innovations," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 315-324, February.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:3:p:315-324
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    References listed on IDEAS

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    1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    2. Somnath Datta & William McCormick, 1998. "Inference for the Tail Parameters of a Linear Process with Heavy Tail Innovations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 337-359, June.
    3. Feigin, Paul D. & Resnick, Sidney I., 1994. "Limit distributions for linear programming time series estimators," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 135-165, June.
    4. de Haan, L. & Pereira, T. Themido, 1999. "Estimating the index of a stable distribution," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 39-55, January.
    5. Davis, Richard A. & McCormick, William P., 1989. "Estimation for first-order autoregressive processes with positive or bounded innovations," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 237-250, April.
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