Testing for parameter instability in predictive regression models

Gorgiev, Iliyan; Harvey, David I.; Leybourne, Stephen J.; Taylor, A.M. Robert

Abstract

We consider tests for structural change, based on the SupF and Cramer-von-Mises type statistics of Andrews (1993) and Nyblom (1989), respectively, in the slope and/or intercept parameters of a predictive regression model where the predictors display strong persistence. The SupF type tests are motivated by alternatives where the parameters display a small number of breaks at deterministic points in the sample, while the Cramer-von-Mises alternative is one where the coefficients are random and slowly evolve through time. In order to allow for an unknown degree of persistence in the predictors, and for both conditional and unconditional heteroskedasticity in the data, we implement the tests using a fixed regressor wild bootstrap procedure. The asymptotic validity of the bootstrap tests is established by showing that the asymptotic distributions of the bootstrap parameter constancy statistics, conditional on the data, coincide with those of the asymptotic null distributions of the corresponding statistics computed on the original data, conditional on the predictors. Monte Carlo simulations suggest that the bootstrap parameter stability tests work well in finite samples, with the tests based on the Cramer-von-Mises type principle seemingly the most useful in practice. An empirical application to U.S. stock returns data demonstrates the practical usefulness of these methods.

Citation

Gorgiev, I., Harvey, D. I., Leybourne, S. J., & Taylor, A. R. (2018). Testing for parameter instability in predictive regression models. Journal of Econometrics, 204(1), https://doi.org/10.1016/j.jeconom.2018.01.005

• Journal Article Type: Article
• Acceptance Date: Jan 10, 2018
• Online Publication Date: Jan 31, 2018
• Publication Date: May 31, 2018
• Deposit Date: Jan 11, 2018
• Publicly Available Date: Jan 31, 2018
• Journal: Journal of Econometrics
• Print ISSN: 0304-4076
• Electronic ISSN: 1872-6895
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 204
• Issue: 1
• DOI: https://doi.org/10.1016/j.jeconom.2018.01.005
• Keywords: Predictive regression; Persistence; Parameter stability tests; Fixed regressor wild bootstrap; Conditional distribution
• Public URL: https://nottingham-repository.worktribe.com/output/935784
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0304407618300095
• Contract Date: Jan 11, 2018