We solve here the general nonstationary multivariate MA spectral factorization problem, i.e. the problem of obtaining all the possible MA models (with time-dependent coefficients) corresponding to a given (time-dependent) autocovariance function. Our result (Theorem 8) relies on a symbolic generalization (Theorem 1) of the classical factorization property of the characteristic polynomial associated with stationary autocovariance functions, and is obtained by means of a matrix extension of ordinary continued fractions. We also give necessary and sufficient conditions for an autocovariance function to be an MA autocovariance function and for a process to be an MA one (Theorems 6 and 7).
Publié le : 1984-03-14
Classification:
Nonstationary time series,
moving average processes,
continued fractions,
spectral factorization,
time varying systems,
62M10,
40A15,
39A70,
93C50
@article{1176346400,
author = {Hallin, Marc},
title = {Spectral Factorization of Nonstationary Moving Average Processes},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 172-192},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346400}
}
Hallin, Marc. Spectral Factorization of Nonstationary Moving Average Processes. Ann. Statist., Tome 12 (1984) no. 1, pp. 172-192. http://gdmltest.u-ga.fr/item/1176346400/