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).
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