2011/12/12 by Hailin Sang, Yan Sun, Sang, Hailin +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F05 #60G10 #62M10 #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Monetary Policy and Economic Impact #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:60F05 #msc:60G10 #msc:62M10 #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1112.2682
to appear in Statistics; 26 pages, 2 figures
openalex publication_date 2011/12/12 · arxiv created 2013/09/21 · arxiv updated 2013/09/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We propose a sparse coefficient estimation and automated model selection procedure for autoregressive (AR) processes with heavy-tailed innovations based on penalized conditional maximum likelihood. Under mild moment conditions on the innovation processes, the penalized conditional maximum likelihood estimator (PCMLE) satisfies a strong consistency, OP(N-1/2) consistency, and the oracle properties, where N is the sample size. We have the freedom in choosing penalty functions based on the weak conditions on them. Two penalty functions, least absolute shrinkage and selection operator (LASSO) and smoothly clipped average deviation (SCAD), are compared. The proposed method provides a distribution-based penalized inference to AR models, which is especially useful when the other estimation methods fail or under perform for AR processes with heavy-tailed innovations (see \citeResnick). A simulation study confirms our theoretical results. At the end, we apply our method to a historical price data of the US Industrial Production Index for consumer goods, and obtain very promising results.