  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 article, the problem of
detecting the change points in a high-dimensional piecewise vector
autoregressive model (VAR) is considered. Reformulated the problem as a
high-dimensional variable selection, a penalized least square estimation using
total variation LASSO penalty is proposed for estimation of model parameters.
It is shown that the developed method over-estimates the number of change
points. A backward selection criterion is thus proposed 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. A block coordinate descent algorithm is developed for
efficient computation of model parameters. The performance of the method is
illustrated using several simulation scenarios.
