MODEL-BUILDING PROBLEM OF PERIODICALLY CORRELATED M-VARIATE MOVING AVERAGE PROCESSES

The model-building problem of periodically correlated nl-variate q-dep endent processes is considered. We show that for a given periodical au tocovariance Function of an m-variate MA(q) process there are two part icular corresponding classes (that may reduce to one class) of periodi c (equivalent) models. Furthermore, any other (intermediate) model is not periodic. It is, however, asymptotically periodic. The matrix coef ficients of the particular periodic models are given in terms of limit s of some periodic matrix continued fractions, which are a generalizat ion of the classical periodic continued fractions (Wall, 1948). These periodic matrix continued fractions are particular solutions of some p rospective and/or retrospective recursion equations, arising from the symbolic factorization of the associated linear autocovariance operato r. In addition, we establish a procedure to calculate these limits. Nu merical examples are given for the simple cases of periodically correl ated univariate one- and two-dependent processes. (C) 1998 Academic Pr ess.