ON STATIONARITY OF THE SOLUTION OF A DOUBLY STOCHASTIC MODEL

. Consider the discrete parameter process {XI} satisfying the doubly stochastic model Xt=otXt-1+et where {o} and {et} are also stochastic processes. Necessary and sufficient conditions on {o} are given for {X1} to be a second order process. When {ot} is a strictly stationary process, some sufficient conditions in terms of {o} are given which guarantee the wide sense stationarity of {Xt}. It turns out that for these problems the distribution and dependence structure of the process {log |o|} play an important role.