Sparse Change-Point VAR models

Abstract

Change-point (CP) VAR models face a dimensionality curse due to the proliferation of parameters that arises when new breaks are detected. To handle large data sets, we introduce the Sparse CP-VAR model that determines which parameters truly vary when a break is detected. By doing so, the number of new parameters to estimate at each regime is drastically reduced and the CP dynamic becomes easier to interpret. The Sparse CP-VAR model disentangles the dynamics of the mean parameters and the covariance matrix. The former uses CP dynamics with shrinkage prior distributions while the latter is driven by an infinite hidden Markov framework. A simulation study highlights that the framework detects correctly the number of breaks per model parameter, and that it takes advantage of common breaks in the cross-sectional dimension to more precisely estimate them. Our applications on financial and macroeconomic systems highlight that the Sparse CP-VAR model helps interpreting the detected breaks. It turns out that many spillover effects have zero regimes meaning that they are zero for the entire sample period. Forecasting wise, the Sparse CP-VAR model is competitive against several recent time-varying parameter and CP-VAR models in terms of log predictive densities.