Likelihood Analysis of a First Order Autoregressive Model with Exponential Innovations

This paper derives the exact distribution of the maximum likelihood estimator of a rst order linear autoregression with an exponential disturbance term. We also show that even if the process is stationary, the estimator is T -consistent, where T is the sample size. In the unit root case the estimator is T -consistent, while in the explosive case the estimator is T -consistent. Further, the likelihood ratio test statistic for a simple hypothesis on the autoregressive parameter is asymptotically uniform for all values of the parameter.