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The robust estimation of autoregressive processes by functional least squares

Published online by Cambridge University Press:  14 July 2016

C. R. Heathcote  and
A. H. Welsh
C. R. Heathcote*
Affiliation:
The Australian National University
A. H. Welsh*
Affiliation:
The Australian National University
*
∗ Postal address for both authors: Department of Statistics, Faculty of Economics, The Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia.
∗ Postal address for both authors: Department of Statistics, Faculty of Economics, The Australian National University, G.P.O. Box 4, Canberra, ACT 2601, Australia.
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Abstract

The stationary autoregressive model but with a long-tailed error distribution is analysed using the method of functional least squares. A family of estimators indexed by a real parameter is obtained and uniform consistency and weak convergence established. The optimum member of the family is chosen to have minimum variance with respect to the parameter, and the parameter value chosen detects and adjusts for long-tailed error distributions. Results of a simulation are given.

Keywords

AUTOREGRESSIONLONG-TAILED ERRORS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 737 - 753
Copyright
Copyright © Applied Probability Trust 1983 

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