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

Abolfazl Safikhani, Ali Shojaie

Abstract:

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative
is to assume piecewise stationarity, where the model is allowed to change at potentially many 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 solve
it using a penalized least square estimator with a total variation penalty. We show that the proposed
penalized estimation method over-estimates the number of change points. We then propose a selection
criterion to identify the change points. 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 studies and real data examples.