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.
Publié le : 1982-06-14
Classification:
Stationary time series,
generalized autoregressive process,
characterization problem,
nonlinear prediction,
62E10,
62M10,
60G10,
60E10
@article{1176345805,
author = {Slud, Eric V.},
title = {A Characterization Problem in Stationary Time Series},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 630-633},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345805}
}
Slud, Eric V. A Characterization Problem in Stationary Time Series. Ann. Statist., Tome 10 (1982) no. 1, pp. 630-633. http://gdmltest.u-ga.fr/item/1176345805/