Penalized Likelihood Estimation in High-Dimensional Time Series Models and its Application

2015/04/25 by Yoshimasa Uematsu, Uematsu, Yoshimasa
Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Monetary Policy and Economic Impact #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.AP #stat.TH

paper · pdf · doi:10.48550/arxiv.1504.06706

This manuscript includes some theoretically insufficient points that will be fixed

openalex publication_date 2015/04/25 · arxiv created 2017/04/26 · arxiv updated 2017/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a general theoretical framework of penalized quasi-maximum likelihood (PQML) estimation in stationary multiple time series models when the number of parameters possibly diverges. We show the oracle property of the PQML estimator under high-level, but tractable, assumptions, comprising the first half of the paper. Utilizing these results, we propose in the latter half of the paper a method of sparse estimation in high-dimensional vector autoregressive (VAR) models. Finally, the usability of the sparse high-dimensional VAR model is confirmed with a simulation study and an empirical analysis on a yield curve forecast.

Citations

• Nearly unbiased variable selection under minimax concave penalty
• A Statistical View of Some Chemometrics Regression Tools

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