ON STATIONARITY OF THE SOLUTION OF A DOUBLY STOCHASTIC MODEL

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