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Maximum likelihood estimation for \(\alpha\)-stable autoregressive processes

Збережено в:
Опубліковано в::arXiv.org (Aug 13, 2009), p. n/a
Автор: Andrews, Beth
Інші автори: Calder, Matthew, Davis, Richard A
Опубліковано:
Cornell University Library, arXiv.org
Предмети:
Monte Carlo simulation
Noise
Economic models
Logarithms
Convergence
Parameter estimation
Constraining
Autoregressive processes
Gaussian process
Maximum likelihood estimation
Asymptotic properties
Autoregressive models
Stock exchanges
Maximum likelihood estimators
Computer simulation
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Короткий огляд:We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian \(\alpha\)-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are \(n^{1/\alpha}\)-consistent and converge in distribution to the maximizer of a random function. The form of this limiting distribution is intractable, but the shape of the distribution for these estimators can be examined using the bootstrap procedure. The bootstrap is asymptotically valid under general conditions. The estimators for the parameters of the stable noise distribution have the traditional \(n^{1/2}\) rate of convergence and are asymptotically normal. The behavior of the estimators for finite samples is studied via simulation, and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of Wal-Mart stock traded daily on the New York Stock Exchange.
ISSN:2331-8422
DOI:10.1214/08-AOS632
Джерело:Engineering Database