BENT NIELSEN and NEIL SHEPHARD
(1999)
'Likelihood analysis of a first order autoregressive model with
exponential innovations'
ABSTRACT:
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 estimator is T^2-consistent, while in the explosive
case the estimator 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.