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Likelihood analysis of a first‐order autoregressive model with exponential innovations
Author(s) -
Nielsen B.,
Shephard N.
Publication year - 2003
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00310
Subject(s) - mathematics , autoregressive model , estimator , unit root , statistics , star model , likelihood ratio test , asymptotic distribution , statistic , autoregressive integrated moving average , time series
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 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 ρ 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.