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STATIONARITY OF THE SOLUTION OF X t = A t X t‐1 +ε t AND ANALYSIS OF NON‐GAUSSIAN DEPENDENT RANDOM VARIABLES
Author(s) -
POURAHMADI MOHSEN
Publication year - 1988
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.1467-9892.1988.tb00467.x
Subject(s) - mathematics , combinatorics , exponential function , branching process , series (stratigraphy) , estimator , gaussian , gaussian process , mathematical analysis , statistics , paleontology , physics , quantum mechanics , biology
. We give general and concrete conditions in terms of the coefficient (stochastic) process {A t } so that the (doubly) stochastic difference equation X t = A t X t‐1 +ε t has a second‐order strictly stationary solution. It turns out that by choosing {A t } and the “innovation” process {ε t } properly, a host of stationary processes with non‐Gaussian marginals and long‐range dependence can be generated using this difference equation. Examples of such nowGaussian marginals include exponential, mixed exponential, gamma, geometric, etc. When {A t } is a binary time series, the conditional least‐squares estimator of the parameters of this model is the same as those of the parameters of a Galton‐Watson branching process with immigration.