STATIONARITY AND CENTRAL LIMIT THEOREM ASSOCIATED WITH BILINEAR TIME SERIES MODELS

摘要

Abstract.Consider the general bilinear times series modelwhere {Xt;t= 0, L1, …} is ap‐variate process,C(px (s+ 1)),A(pxp).Bt(pxp) (1 ≤j≤q) are arbitrary matrices of constants, εT=εt,…εt‐q+1 and {εt; t=0, ±1, …} is a strictly stationary ergodic sequence of random variables. We investigate a set of minimal regularity conditions (onC, A, Bjand {εt}) under which we can establish the existence and causality ofXtand the asymptotic normality of the sample mea