Abstrac t . Some simple models are introduced which may be used for modelling or generating sequences of dependent discrete random variables with generalized Poisson marginal distribution. Our approach for building these models is similar to that of the Poisson ARMA processes considered by Al-Osh and Alzaid (1987, J. Time Ser. Anal., 8, 261-275; 1988, Statist. Hefte, 29, 281-300) and McKenzie (...

In the present paper the necessary and sufficient conditions for the estimates of covariance coefficients of moving average processes are presented. Further the modification for estimates of Wilson's method covariance coefficients is introduced.

In the last few years Ayache, Esser and Hamonier introduced a new Multifractional Process with Random Exponent (MPRE) obtained by replacing Hurst parameter in moving average representation of Fractional Brownian Motion through Wiener integral an adapted Hölder continuous stochastic process indexed integration variable. Thus, this MPRE can be expressed as Itô which is considerable advantage resp...

We investigate how large deviations events cluster in the framework of an infinite moving average process with light-tailed noise and long memory. The memory makes clusters larger, asymptotic behaviour size turns out to be described by first hitting time a randomly shifted fractional Brownian motion drift.