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ON STATIONARITY OF THE SOLUTION OF A DOUBLY STOCHASTIC MODEL
Author(s) -
Pourahmadi Mohsen
Publication year - 1986
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1986.tb00490.x
Subject(s) - mathematics , stochastic process , stochastic ordering , order (exchange) , process (computing) , stochastic modelling , continuous time stochastic process , stationary process , distribution (mathematics) , pure mathematics , statistical physics , mathematical analysis , statistics , computer science , finance , economics , operating system , physics
. Consider the discrete parameter process {X I } satisfying the doubly stochastic model X t =ø t X t‐1 +ε t where {ø} and {ε t } are also stochastic processes. Necessary and sufficient conditions on {ø} are given for { X 1 } 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.