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First-order autoregressive models for gamma and exponential processes

Published online by Cambridge University Press:  14 July 2016

C. H. Sim
C. H. Sim*
Affiliation:
University of Malaya
*
∗Postal address: Department of Mathematics, Faculty of Science, University of Malaya, 59100 Kuala Lumpur, Malaysia.
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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.

Keywords

CORRELATION STRUCTURESSTOCHASTIC DIFFERENCE EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 325 - 332
Copyright
Copyright © Applied Probability Trust 1990 

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