Department of Statistics
Joint Structural Break Detection and Parameter Estimation in High-Dimensional Non-Stationary VAR Models
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. In this talk, 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. This is a joint work with Ali Shojaie.
Refreshments at 3:45pm in Snedecor 2101.