# Likelihood Analysis of a First Order Autoregressive Model With Exponential Innovations

Nuffield College, University of Oxford Working Paper No. 1999-w8

Posted: 8 Apr 1999

See all articles by Bent Nielsen

## Bent Nielsen

University of Oxford - Department of Economics

## Neil Shephard

Harvard University

Date Written: March 30, 1999

### 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.

JEL Classification: C10, C12

Suggested Citation

Nielsen, Bent and Shephard, Neil, Likelihood Analysis of a First Order Autoregressive Model With Exponential Innovations (March 30, 1999). Nuffield College, University of Oxford Working Paper No. 1999-w8. Available at SSRN: https://ssrn.com/abstract=158228

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