Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models

TL;DR

This paper introduces a three-stage method for accurately detecting change points and estimating parameters in high-dimensional, piecewise stationary VAR models, addressing the limitations of assuming stationarity.

Contribution

It proposes a novel three-stage procedure combining penalized estimation and backward selection for consistent change point detection and parameter estimation in high-dimensional VAR models.

Findings

The method accurately detects the number and locations of change points.

It consistently estimates VAR parameters within each segment.

Performance validated through simulations and real data examples.

Abstract

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. We propose a three-stage procedure for consistent estimation of both structural change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and propose a penalized least square estimator using a total variation penalty. We show that the proposed penalized estimation method over-estimates the number of change points. We then propose a backward selection criterion in conjunction with a penalized least square estimator to tackle this issue. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We prove that the proposed procedure consistently detects the number of change points and their locations. We also show that the procedure consistently estimates the VAR parameters. The performance of the method is illustrated through several simulation scenarios and real data examples.