Likelihood analysis of a first‐order autoregressive model with exponential innovations
- 19 May 2003
- journal article
- Published by Wiley in Journal of Time Series Analysis
- Vol. 24 (3) , 337-344
- https://doi.org/10.1111/1467-9892.00310
Abstract
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 isT‐consistent, whereTis the sample size. In the unit root case, the estimator isT2‐consistent, while, in the explosive case, the estimator isρT‐consistent. Further, the likelihood ratio test statistic for a simple hypothesis on the autoregressive parameter is asymptotically uniform for all values of the parameter.Keywords
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