ON STATIONARITY OF THE SOLUTION OF A DOUBLY STOCHASTIC MODEL

Mohsen Pourahmadi

Journal of Time Series Analysis, 1986, vol. 7, issue 2, 123-131

Abstract: Abstract. Consider the discrete parameter process {XI} satisfying the doubly stochastic model Xt=øtXt‐1+εt where {ø} and {εt} are also stochastic processes. Necessary and sufficient conditions on {ø} are given for {X1} to be a second order process. When {øt} is a strictly stationary process, some sufficient conditions in terms of {ø} 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 |ø|} play an important role.

Date: 1986
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