First-order autoregressive models for gamma and exponential processes

Abstract

In this paper we propose an autoregressive representation for a particular type of stationary Gamma(θ–1, v) process whose n-dimensional joint distributions have Laplace transform |In + θSnVn|–v, where Sn = diag(s1, · ··, sn), Vn is an n × n positive definite matrix with elements υ ij = p|i–j|i2, i, j = 1, ···, n and p is the lag-1 autocorrelation of the gamma process. We also generalize the two-parameter NEAR(1) model of Lawrance and Lewis (1981) to an exponential first-order autoregressive model with three parameters. The correlation structure and higher-order properties of the two proposed models are also given.