## The Annals of Statistics

### Recursive Computation of $M$-Estimates for the Parameters of a Finite Autoregressive Process

Katherine Campbell

#### Abstract

Stochastic approximation methods are used to generate a sequence of "$M$-estimates" for the unknown parameters of an autoregressive process of known, finite order which may have heavy-tailed innovations. Weak dependence properties, which can be demonstrated for many autoregressive processes, are used in the proof that the sequence converges almost surely to the parameters. A brief Monte Carlo study verifies that bounded influence functions provide protection for recursive procedures against heavy-tailed innovations.

#### Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 442-453.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345785

Digital Object Identifier
doi:10.1214/aos/1176345785

Mathematical Reviews number (MathSciNet)
MR653519

Zentralblatt MATH identifier
0492.62076

JSTOR

#### Citation

Campbell, Katherine. Recursive Computation of $M$-Estimates for the Parameters of a Finite Autoregressive Process. Ann. Statist. 10 (1982), no. 2, 442--453. doi:10.1214/aos/1176345785. https://projecteuclid.org/euclid.aos/1176345785