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

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.