The Annals of Statistics

Spectral Factorization of Nonstationary Moving Average Processes

Marc Hallin

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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).

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

First available in Project Euclid: 12 April 2007

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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

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


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

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