Autoregressive model selection with simultaneous sparse coefficient estimation

Details Autoregressive model selection with simultaneous sparse coefficient estimation Autoregressive model selection with simultaneous sparse coefficient estimation

2011-12-12

arxiv.org/abs/1112.2682v1

Statistics

Methodology

23 pages, 6 figures

Scientific paper

In this paper we propose a sparse coefficient estimation procedure for autoregressive (AR) models based on penalized conditional maximum likelihood. The penalized conditional maximum likelihood estimator (PCMLE) thus developed has the advantage of performing simultaneous coefficient estimation and model selection. Mild conditions are given on the penalty function and the innovation process, under which the PCMLE satisfies a strong consistency, local $N^{-1/2}$ consistency, and oracle property, respectively, where N is sample size. Two penalty functions, least absolute shrinkage and selection operator (LASSO) and smoothly clipped average deviation (SCAD), are considered as examples, and SCAD is shown to have better performances than LASSO. A simulation study confirms our theoretical results. At the end, we provide an application of our method to a historical price data of the US Industrial Production Index for consumer goods, and the result is very promising.

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