STATIONARITY OF THE SOLUTION OF Xt= AtXt‐1+εt AND ANALYSIS OF NON‐GAUSSIAN DEPENDENT RANDOM VARIABLES

Mohsen Pourahmadi

Journal of Time Series Analysis, 1988, vol. 9, issue 3, 225-239

Abstract: Abstract. We give general and concrete conditions in terms of the coefficient (stochastic) process {At} so that the (doubly) stochastic difference equation Xt= AtXt‐1+εt has a second‐order strictly stationary solution. It turns out that by choosing {At} and the “innovation” process {εt} 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 {At} 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.

Date: 1988
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