The Annals of Statistics
- Ann. Statist.
- Volume 12, Number 1 (1984), 172-192.
Spectral Factorization of Nonstationary Moving Average Processes
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).
Ann. Statist., Volume 12, Number 1 (1984), 172-192.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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