First-order autoregressive models for gamma and exponential processes
- 1 June 1990
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 27 (2) , 325-332
- https://doi.org/10.2307/3214651
Abstract
In this paper we propose an autoregressive representation for a particular type of stationary Gamma(θ–1,v) process whosen-dimensional joint distributions have Laplace transform |In+θSnVn|–v, whereSn=diag(s1, · ··,sn),Vnis ann×npositive definite matrix with elementsυij= p|i–j|i2,i, j =1, ···,nandpis 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
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