Fast and Flexible Bayesian Inference in Time-varying Parameter Regression Models

TL;DR

This paper introduces a hierarchical mixture model for time-varying parameter regression that captures multiple regimes and structural breaks, offering faster computation and improved forecasting accuracy over traditional methods.

Contribution

It proposes a novel hierarchical mixture approach for TVP regression that mimics regime changes, along with efficient Bayesian inference techniques for large datasets.

Findings

The methods are accurate and significantly faster than standard approaches.

The models outperform alternatives in inflation forecasting.

Different parameter change patterns are identified compared to random walk assumptions.

Abstract

In this paper, we write the time-varying parameter (TVP) regression model involving K explanatory variables and T observations as a constant coefficient regression model with KT explanatory variables. In contrast with much of the existing literature which assumes coefficients to evolve according to a random walk, a hierarchical mixture model on the TVPs is introduced. The resulting model closely mimics a random coefficients specification which groups the TVPs into several regimes. These flexible mixtures allow for TVPs that feature a small, moderate or large number of structural breaks. We develop computationally efficient Bayesian econometric methods based on the singular value decomposition of the KT regressors. In artificial data, we find our methods to be accurate and much faster than standard approaches in terms of computation time. In an empirical exercise involving inflation forecasting using a large number of predictors, we find our models to forecast better than alternative approaches and document different patterns of parameter change than are found with approaches which assume random walk evolution of parameters.