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Assuming stationarity is unrealistic in many time series applications. A morerealistic alternative is to allow for piecewise stationarity, where the modelis allowed to change at given time points. We propose a three-stage procedurefor consistent estimation of both structural change points and parameters ofhigh-dimensional piecewise vector autoregressive (VAR) models. In the firststep, we reformulate the change point detection problem as a high-dimensionalvariable selection one, and propose a penalized least square estimator using atotal variation penalty. We show that the proposed penalized estimation methodover-estimates the number of change points. We then propose a backwardselection criterion in conjunction with a penalized least square estimator totackle this issue. In the last step of our procedure, we estimate the VARparameters in each of the segments. We prove that the proposed procedureconsistently detects the number of change points and their locations. We alsoshow that the procedure consistently estimates the VAR parameters. Theperformance of the method is illustrated through several simulation scenariosand real data examples.

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