Estimation of AR and ARMA models by stochastic complexity

Details Estimation of AR and ARMA models by stochastic complexity Estimation of AR and ARMA models by stochastic complexity

2007-02-26

arxiv.org/abs/math/0702765v1

IMS Lecture Notes Monograph Series 2006, Vol. 52, 48-59

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000941 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000000941

In this paper the stochastic complexity criterion is applied to 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 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.

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