Likelihood analysis 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 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-super-2-consistent, while, in the explosive case, the estimator is rho-super-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. Copyright 2003 Blackwell Publishing Ltd.