Abstract.Gaver and Lewis and Lawrance and Lewis have described an autoregressive process of orderp, EAR(p), which is such that the marginal distribution of the observations follows an exponential distribution. There is now a rich class of exponential and related distributions time series models. Such models are of importance in queuing and network processes, for example. The properties of these and related models have been well explored, but so far little work has been done toward the important problem of estimation. We attempt here to address this question for the EAR(p) models. Because of inherent discontinuities in some of the relevant underlying distributions, the standard theory cannot be applied. However, by utilizing a general theory developed by Klimko and Nelson, conditional least‐squares estimators are derived. Further, it is shown that these estimators are strongly consistent and asymptotically normally distributed. Small‐sample properties are investigated. The results suggest that these estimators are to be preferred compared with those suggested by Lawrance and Le
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