Testing for Structural Change under Nonstationarity

TL;DR

This paper derives the asymptotic distributions of structural break test statistics in predictive regression models with nonstationary regressors, considering different model specifications including intercepts and persistent regressors.

Contribution

It provides new theoretical results on the asymptotic behavior of structural break tests in models with mildly integrated or persistent regressors, extending previous frameworks.

Findings

Derived asymptotic distributions for test statistics with persistent regressors

Analyzed effects of including or excluding intercepts in the models

Set the stage for further empirical validation and applications

Abstract

This Appendix (dated: July 2021) includes supplementary derivations related to the main limit results of the econometric framework for structural break testing in predictive regression models based on the OLS-Wald and IVX-Wald test statistics, developed by Katsouris C (2021). In particular, we derive the asymptotic distributions of the test statistics when the predictive regression model includes either mildly integrated or persistent regressors. Moreover, we consider the case in which a model intercept is included in the model vis-a-vis the case that the predictive regression model has no model intercept. In a subsequent version of this study we reexamine these particular aspects in more depth with respect to the demeaned versions of the variables of the predictive regression.