Testing for structural changes in linear regressions with time-varying variance

Abstract

This article proposes a nonparametric test for structural changes in linear regression models that allows for serial correlation, autoregressive conditional heteroskedasticity and time-varying variance in error terms. The test requires no trimming of the boundary region near the end points of the sample period, and requires no prior information on the alternative, what it requires is the transformed OLS residuals under the null hypothesis. We show that the test has a limiting standard normal distribution under the null hypothesis, and is powerful against single break, multiple breaks and smooth structural changes. The Monte Carlo experiment is conducted to highlight the merits of the proposed test relative to other popular tests for structural changes.

Keywords:

• U-statistic
• structural changes
• time-varying variance
• bandwidth selection

Acknowledgments

We are grateful to the conference participants of International Econometrics Conference at Shandong University for helpful comments. Erhua Zhang acknowledges the support from K. C. Wong Magna Fund in Ningbo University. Jilin Wu acknowledges the support from the National Natural Science Foundation of China (#71571110).

Notes

1 When X_t contains only a constant, our null hypothesis is now interpreted as testing for changing mean, then one key problem of testing for changing mean is non-monotonic power. Evidence from Vogelsang (1999) indicates that an important source of nonmonotonic power comes from the bias in estimated AR parameters when there is a change in the deterministic component. When the alternative hypothesis is close to the null, the estimation bias is usually small and has little effect on the power of the test. However, the bias in estimating parameters has a substantial effect on reducing the power when the alternative is distant from the null. Juhl and Xiao (2005) also give detailed disscusion and suggest detrending the original data nonparametrically first; the AR parameters can then be estimated consistently based on the nonparametrically detrended data even if there is a change in the deterministic mean.