When is an altoregressive scheme stationary

1 January 1973

journal article
research article
Published by Taylor & Francis in Communications in Statistics

Vol. 1 (6) , 533-544
https://doi.org/10.1080/03610927308827046

Abstract

We show that a sufficient condition for an autoregrassive scheme to be stationary is that the roots of the indicia1 polynomial lie within the unit circle. The importance of this theorem is that its proof yields some interesting results. The main ones are: (i) when fitting an autoregressive scheme via the Yule-Walker equations, the fitted scheme is guaranteed to be stationary, and (ii) an easily applicable test to check whether a given scheme is stationary or not is found.

Keywords

This publication has 9 references indexed in Scilit:

Multiple Time Series
Wiley Series in Probability and Statistics, 1970
On Linear Difference Equations
The American Mathematical Monthly, 1968
On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix
Biometrika, 1963
An Approach to Time Series Analysis
The Annals of Mathematical Statistics, 1961
The Fitting of Time-Series Models
Revue de l'Institut International de Statistique / Review of the International Statistical Institute, 1960
On the Inversion of the Sample Covariance Matrix in a Stationary Autoregressive Process
The Annals of Mathematical Statistics, 1958
Statistical Analysis of Stationary Time Series
Physics Today, 1957
Stationarity conditions for stochastic processes of the autoregressive and moving-average type
Biometrika, 1956
Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1917