Estimation of AR and ARMA models by stochastic complexity. (English) Zbl 1268.62113

Ho, Hwai-Chung (ed.) et al., Time series and related topics. In memory of Ching-Zong Wei. Selected papers based on the presentations at the conference, Taipei, Taiwan, December 12–14, 2005. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 978-0-940600-68-3/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 52, 48-59 (2006).
Summary: In this paper the stochastic complexity criterion is applied to the estimation of the order in AR and ARMA models. The power of the criterion for short strings is illustrated by simulations. It requires an integral of the square root of Fisher information, which is done by a Monte Carlo technique. The stochastic complexity, which is the negative logarithm of the normalized maximum likelihood universal density function, is given. Also, exact asymptotic formulas for the Fisher information matrix are derived.
For the entire collection see [Zbl 1113.62001].


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M09 Non-Markovian processes: estimation
62H12 Estimation in multivariate analysis
62F10 Point estimation
65C05 Monte Carlo methods
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