Bayesian high-dimensional regression for change point analysis

In many econometrics applications, the dataset under investigation spans heterogeneous regimes that are more appropriately modeled using piece-wise components for each of the data segments separated by change-points. We consider using Bayesian high-dimensional shrinkage priors in a change point setting to understand segment-specific relationship between the response and the covariates. Covariate selection before and after each change point can identify possibly different sets of relevant covariates, while the fully Bayesian approach ensures posterior inference for the change points is also available. We demonstrate the flexibility of the approach for imposing different variable selection constraints like grouping or partial selection and discuss strategies to detect an unknown number of change points. Simulation experiments reveal that this simple approach delivers accurate variable selection, and inference on location of the change points, and substantially outperforms a frequentist lasso-based approach, uniformly across a wide range of scenarios. Application of our model to Minnesota house price dataset reveals change in the relationship between house and stock prices around the sub-prime mortgage crisis.