First-order autoregressive gamma sequences and point processes 论文

摘要

It is shown that there is an innovation process {∊ n } such that the sequence of random variables { X n } generated by the linear, additive first-order autoregressive scheme X n = p X n-1 + ∊ n are marginally distributed as gamma (λ, k ) variables if 0 ≦ p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.