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

TL;DR

This paper develops a theoretical framework for penalized likelihood estimation in high-dimensional stationary time series models, demonstrating oracle properties and proposing a sparse VAR estimation method validated through simulations and yield curve forecasting.

Contribution

It introduces a novel theoretical framework for PQML estimation in high-dimensional time series and proposes a practical sparse VAR estimation method with empirical validation.

Findings

Oracle property of PQML estimator established

Sparse VAR models effectively forecast yield curves

Method performs well in simulations and real data

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.