Techniques for Testing the Constancy of Regression Relationships Over Time

TLDR

Methods for assessing the stability of regression relationships over time are reviewed. The authors introduce recursive residuals and develop cusum and cusum‑of‑squares tests, explore moving‑regression and time‑varying coefficient models, consider the Quandt log‑likelihood ratio statistic, and emphasize graphical diagnostics. The techniques are implemented in the computer program timvar and demonstrated on three data sets.

Abstract

Summary Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are polynomials in time are studied. The Quandt log-likelihood ratio statistic is considered. Emphasis is placed on the use of graphical methods. The techniques proposed have been embodied in a comprehensive computer program, timvar. Use of the techniques is illustrated by applying them to three sets of data.