Autoregressive Process Modeling via the Lasso Procedure

TL;DR

This paper investigates the use of the Lasso method for fitting autoregressive models, providing theoretical guarantees for model selection, estimation, and prediction consistency under increasing lag sizes.

Contribution

It offers new theoretical results on the consistency of the Lasso estimator in autoregressive models with growing lag lengths.

Findings

Lasso achieves model selection consistency under certain conditions.

The estimator is estimation consistent as sample size increases.

Prediction accuracy improves with the proposed framework.

Abstract

The Lasso is a popular model selection and estimation procedure for linear models that enjoys nice theoretical properties. In this paper, we study the Lasso estimator for fitting autoregressive time series models. We adopt a double asymptotic framework where the maximal lag may increase with the sample size. We derive theoretical results establishing various types of consistency. In particular, we derive conditions under which the Lasso estimator for the autoregressive coefficients is model selection consistent, estimation consistent and prediction consistent. Simulation study results are reported.