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