When regression coefficients change over time: A proposal

TL;DR

This paper introduces a state space model to capture how regression coefficients evolve over time, addressing the assumption of static relationships in forecasting and highlighting the impact of changing dynamics on prediction uncertainty.

Contribution

It proposes a novel method for modeling time-varying regression coefficients using state space techniques, improving understanding of dynamic relationships in forecasting.

Findings

Accurate estimates for continuous outcomes

Method fails for binary outcomes

Highlights uncertainty due to changing dynamics

Abstract

A common approach in forecasting problems is to estimate a least-squares regression (or other statistical learning models) from past data, which is then applied to predict future outcomes. An underlying assumption is that the same correlations that were observed in the past still hold for the future. We propose a model for situations when this assumption is not met: adopting methods from the state space literature, we model how regression coefficients change over time. Our approach can shed light on the large uncertainties associated with forecasting the future, and how much of this is due to changing dynamics of the past. Our simulation study shows that accurate estimates are obtained when the outcome is continuous, but the procedure fails for binary outcomes.