## The Annals of Statistics

### A Characterization Problem in Stationary Time Series

Eric V. Slud

#### Abstract

If a strictly stationary process $\{Z_k\}$ has residuals $Z_{k+1} - \sum^k_{j=1} a_{k,j}Z_j$ independent of $(Z_1, \cdots, Z_k)$ for all $k \geq m$, it is shown that the process is Gaussian or degenerate or $m$-step Markovian. Generalized (nonlinear) autoregressive stationary processes are defined and partially characterized.

#### Article information

Source
Ann. Statist., Volume 10, Number 2 (1982), 630-633.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345805

Digital Object Identifier
doi:10.1214/aos/1176345805

Mathematical Reviews number (MathSciNet)
MR653539

Zentralblatt MATH identifier
0488.62066

JSTOR