Suppose that a three-dimensional VARMA process ???????? has Kronecker indices ????1 = 3, ????2 = 1, and ????3 = 2.

(a) Write the form of the coefficient matrices ????#

???? and ????#

???? in the echelon canonical ARMA model structure of equation (14.7.1) for this process.

(b) For this process {????????}, describe the nature of the zero canonical correlations that occur in the canonical correlation analysis of the past vector

???? ???? = (????′

????

, ????′

????−1, …)′ and various future vectors ????∗

????+1.

(c) Write the form of the minimal dimension echelon state-space model corresponding to the echelon canonical ARMA model for this process.