Title: Consistent change-point detection and parameter estimation in high-dimensional piecewise-stationary VAR models
Authors: Ali Shojaie - University of Washington (United States) [presenting]
Abolfazl Safikhani - University of Florida (United States)
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 consider the problem of detecting the change points and estimation of model parameters in a high-dimensional piecewise vector autoregressive model (VAR). To this end, we propose a two-stage estimation strategy for consistent estimation of both the change points, as well as the parameters of the VAR process. 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 thus propose a backward selection criterion in conjunction with the penalized least square estimator to tackle this issue. We prove that the proposed two-stage procedure consistently detects the number of change points and their locations. We also show that the procedure results in consistent estimation of VAR parameters. A block coordinate descent algorithm is developed for efficient computation of model parameters. The performance of the method is illustrated using several simulation scenarios, and real data examples.