We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral characterizations for this property from univariate processes to multivariate processes.

This paper considers the maximum likelihood estimation (MLE) of a class of stationary and invertible vector autoregressive fractionally integrated moving-average (VARFIMA) processes considered in (26) of Luceño [1] or Model A of Lobato [2] where each component yi,t is a fractionally integrated process of order di, i = 1, . . . , r. Under the conditions outlined in Assumption 1 of this paper, th...

This paper elucidates the connection between stationary symmetric α-stable processes with 0 < α < 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that a necessary and sufficient for a stationary stable process to be ergodic is that its p...