Reduced-rank Envelope Vector Autoregressive Models

TL;DR

This paper introduces the reduced-rank envelope VAR (REVAR) model, combining reduced-rank and envelope methods to improve efficiency and accuracy in high-dimensional time series analysis.

Contribution

It proposes a novel REVAR model that integrates reduced-rank and envelope VAR techniques, addressing inefficiencies and rank deficiency issues in existing models.

Findings

REVAR outperforms traditional VAR models in simulations.

REVAR achieves higher estimation accuracy and efficiency.

Real data analysis confirms REVAR's practical advantages.

Abstract

The standard vector autoregressive (VAR) models suffer from overparameterization which is a serious issue for high-dimensional time series data as it restricts the number of variables and lags that can be incorporated into the model. Several statistical methods, such as the reduced-rank model for multivariate (multiple) time series (Velu et al., 1986; Reinsel and Velu, 1998; Reinsel et al., 2022) and the Envelope VAR model (Wang and Ding, 2018), provide solutions for achieving dimension reduction of the parameter space of the VAR model. However, these methods can be inefficient in extracting relevant information from complex data, as they fail to distinguish between relevant and irrelevant information, or they are inefficient in addressing the rank deficiency problem. We put together the idea of envelope models into the reduced-rank VAR model to simultaneously tackle these challenges, and propose a new parsimonious version of the classical VAR model called the reduced-rank envelope VAR (REVAR) model. Our proposed REVAR model incorporates the strengths of both reduced-rank VAR and envelope VAR models and leads to significant gains in efficiency and accuracy. The asymptotic properties of the proposed estimators are established under different error assumptions. Simulation studies and real data analysis are conducted to evaluate and illustrate the proposed method.