Statistical analysis of multiple moving average processes using periodicity

(1-2) Pj(t) = Pj(t + d) , qt = qt+d and {E,} is a normal white noise with zero mean value and a variance a. Such process is natural analogy of the periodic autoregressive process (see e.g. [ l ] , [5], [6], [7]) and therefore the idea originates to use the estimation technique described in [3] for the treatment of the multiple moving average models (the same approach to the multiple autoregressive models is presented in [5] and [6]). Let us consider a d-dimensional moving average process {A"r} of an order q. The corresponding model can be written in the form