The Annals of Statistics

Spectral Factorization of Nonstationary Moving Average Processes

Marc Hallin

Full-text: Open access

Abstract

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).

Article information

Source
Ann. Statist., Volume 12, Number 1 (1984), 172-192.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346400

Digital Object Identifier
doi:10.1214/aos/1176346400

Mathematical Reviews number (MathSciNet)
MR733507

Zentralblatt MATH identifier
0538.62076

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 40A15: Convergence and divergence of continued fractions [See also 30B70] 39A70: Difference operators [See also 47B39] 93C50

Keywords
Nonstationary time series moving average processes continued fractions spectral factorization time varying systems

Citation

Hallin, Marc. Spectral Factorization of Nonstationary Moving Average Processes. Ann. Statist. 12 (1984), no. 1, 172--192. doi:10.1214/aos/1176346400. https://projecteuclid.org/euclid.aos/1176346400


Export citation