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Abstract:
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We consider maximum likelihood estimation for the parameters of autoregressive time series processes with non-Gaussian $\alpha$-stable noise. Both causal and noncausal autoregressive models are considered. Applications for these time series models have appeared, for example, in the fields of economics and finance, signal processing, and teletraffic engineering. We give a nondegenerate limiting distribution for consistent maximum likelihood estimators of model parameters. The estimators for the autoregressive model parameters are $n^{1/\alpha}$-consistent, while the estimators for the parameters of the stable noise distribution have the traditional $n^{1/2}$ rate of convergence. The behavior of the estimators for finite samples is studied via simulation, and maximum likelihood estimation is used to fit a noncausal autoregressive model to stock market trading volume data.
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