Likelihood Anlaysis of a First Order Autoregressive Model with Exponential Innovations

This paper derives the exact distribution of the maximum likelihood estimator of a first order linear autoregression with exponential innovations. We 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 estimate is T^2-consistent, while in the explosive case the estimate is rho^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.