  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.
