STATIONARITY OF THE SOLUTION OF Xt= AtXt1+t AND ANALYSIS OF NONGAUSSIAN DEPENDENT RANDOM VARIABLES Academic Article

abstract

• Abstract. We give general and concrete conditions in terms of the coefficient (stochastic) process {At} so that the (doubly) stochastic difference equation Xt= AtXt1+t has a secondorder strictly stationary solution. It turns out that by choosing {At} and the innovation process {t} properly, a host of stationary processes with nonGaussian marginals and longrange 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 leastsquares estimator of the parameters of this model is the same as those of the parameters of a GaltonWatson branching process with immigration. Copyright 1988, Wiley Blackwell. All rights reserved

authors

• Pourahmadi, Mohsen

published proceedings

• Journal of Time Series Analysis

author list (cited authors)

• POURAHMADI, M.

citation count

• 34

complete list of authors

• POURAHMADI, MOHSEN

publication date

• January 1988

publisher

• Wiley  Publisher

published in

• Journal of Time Series Analysis  Journal

Digital Object Identifier (DOI)

• 10.1111/j.1467-9892.1988.tb00467.x

start page

• 225

end page

• 239

volume

• 9

issue

• 3

URL

• http%3A%2F%2Fdx.doi.org%2F10.1111%2Fj.1467-9892.1988.tb00467.x