The Annals of Statistics

A Characterization Problem in Stationary Time Series

Eric V. Slud

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G10: Stationary processes 60E10: Characteristic functions; other transforms

Keywords
Stationary time series generalized autoregressive process characterization problem nonlinear prediction

Citation

Slud, Eric V. A Characterization Problem in Stationary Time Series. Ann. Statist. 10 (1982), no. 2, 630--633. doi:10.1214/aos/1176345805. https://projecteuclid.org/euclid.aos/1176345805


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