A NOTE ON THE DISTRIBUTIONS OF NON‐LINEAR AUTOREGRESSIVE STOCHASTIC MODELS

1 January 1981

journal article
Published by Wiley in Journal of Time Series Analysis

Vol. 2 (1) , 49-52
https://doi.org/10.1111/j.1467-9892.1981.tb00310.x

Abstract

It is shown that an ergodic stationary non‐linear autoregressive stochastic process, perturbed by a white noise process with symmetric distributions, has symmetric stationary distributions if and only if the regression function is skew‐symmetric. The implications of this observation are discussed.

Keywords

NON‐LINEAR AUTOREGRESSION
SYMMETRIC DISTRIBUTIONS
HIGHER ORDER SPECTRA
LINEARITY TEST
SYMMETRY TEST

This publication has 3 references indexed in Scilit:

A TEST FOR LINEARITY OF STATIONARY TIME SERIES
Journal of Time Series Analysis, 1980
Nonlinear autoregressive processes
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1978
An Introduction to Polyspectra
The Annals of Mathematical Statistics, 1965