Bayesian High-Dimensional Regression for Change Point Analysis.

Area of Science:

• Econometrics
• Statistical Modeling
• Bayesian Inference

Background:

• Econometric datasets often exhibit heterogeneous regimes requiring piecewise modeling.
• Change points delineate segments with distinct relationships between response and covariates.
• Accurate identification of these segments and their specific covariate relationships is crucial.

Purpose of the Study:

• To develop a Bayesian framework for analyzing heterogeneous data segments separated by change points.
• To perform segment-specific covariate selection in a high-dimensional setting.
• To provide robust inference on change point locations and associated covariate effects.

Main Methods:

• Utilizing Bayesian high-dimensional shrinkage priors within a change point framework.
• Implementing fully Bayesian inference for both covariate selection and change point localization.
• Exploring strategies for detecting an unknown number of change points and imposing variable selection constraints.

Main Results:

• The proposed Bayesian approach achieves accurate variable selection and precise inference on change point locations.
• It demonstrates superior performance compared to frequentist lasso-based methods across various scenarios.
• Application to housing data revealed significant shifts in house-stock price relationships around the sub-prime crisis.

Conclusions:

• The Bayesian change point model offers a flexible and powerful tool for analyzing complex econometric data.
• It effectively identifies segment-specific covariate relationships and change point dynamics.
• The approach provides a significant advancement over existing frequentist methods for regime-dependent analysis.