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Least absolute deviation estimates in autoregression with infinite variance

Published online by Cambridge University Press:  14 July 2016

S. Gross  and
W. L. Steiger
S. Gross*
Affiliation:
Baruch College, City University of New York
W. L. Steiger*
Affiliation:
Rutgers University
*
∗Postal address: Department of Statistics, Baruch College, City University of New York, Box 344, 46 E. 26th St. N.Y. 10010, U.S.A.
∗∗Postal address: Department of Computer Science, Hill Center for the Mathematical Sciences, Rutgers University, New Brunswick, N.J. 08903, U.S.A.
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Abstract

We consider an L1 analogue of the least squares estimator for the parameters of stationary, finite-order autoregressions. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. The striking feature is that the conditions are so mild as to include processes with infinite variance, notably the stationary, finite autoregressions driven by stable increments in Lα, α > 1. Finally, sampling properties of LAD are compared to those of least squares. Together with a known convergence rate result for least squares, the Monte Carlo study provides evidence for a conjecture on the convergence rate of LAD.

Keywords

LEAST ABSOLUTE DEVIATIONAUTOREGRESSIONINFINITE VARIANCE
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979 , pp. 104 - 116
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

Research supported in part by a grant from the Rutgers University Research Council.

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