STATIONARITY OF THE SOLUTION OF Xt= AtXt‐1+εtAND ANALYSIS OF NON‐GAUSSIAN DEPENDENT RANDOM VARIABLES
- 1 May 1988
- journal article
- Published by Wiley in Journal of Time Series Analysis
- Vol. 9 (3) , 225-239
- https://doi.org/10.1111/j.1467-9892.1988.tb00467.x
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+εthas 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.Keywords
This publication has 23 references indexed in Scilit:
- Autoregressive moving-average processes with negative-binomial and geometric marginal distributionsAdvances in Applied Probability, 1986
- ON STATIONARITY OF THE SOLUTION OF A DOUBLY STOCHASTIC MODELJournal of Time Series Analysis, 1986
- A RANDOM PARAMETER PROCESS FOR MODELING AND FORECASTING TIME SERIESJournal of Time Series Analysis, 1986
- SOME DOUBLY STOCHASTIC TIME SERIES MODELSJournal of Time Series Analysis, 1986
- A new Laplace second-order autoregressive time-series model--NLAR(2)IEEE Transactions on Information Theory, 1985
- THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELSJournal of Time Series Analysis, 1983
- A new autoregressive time series model in exponential variables (NEAR(1))Advances in Applied Probability, 1981
- Fractional DifferencingBiometrika, 1981
- AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCINGJournal of Time Series Analysis, 1980
- A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)Advances in Applied Probability, 1977