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June, 1982 A Characterization Problem in Stationary Time Series
Eric V. Slud
Ann. Statist. 10(2): 630-633 (June, 1982). DOI: 10.1214/aos/1176345805


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.


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Eric V. Slud. "A Characterization Problem in Stationary Time Series." Ann. Statist. 10 (2) 630 - 633, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0488.62066
MathSciNet: MR653539
Digital Object Identifier: 10.1214/aos/1176345805

Primary: 62E10
Secondary: 60E10 , 60G10 , 62M10

Keywords: characterization problem , generalized autoregressive process , nonlinear prediction , stationary time series

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
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