Testing for a unit root with nonstationary nonlinear heteroskedasticity

Abstract

We provide a large sample theory for the Dickey-Fuller unit root test when the volatility process is driven by a nonlinear transformation of nonstationary time series. Our theory allows the dynamics of future volatilities being affected by the current shock, and involves replacing the nuisance nonlinear function by its consistent kernel estimator. This improves the existing literature for unit root testing with heteroskedasticity by using external data explicitly. We further propose a valid bootstrap procedure to implement the test, which is found to perform well in finite samples. A real data example is also provided

Keywords:

• Conditional heteroskedasticity
• leverage effect
• nonparametric
• unit root test

JEL classification:

• C12
• C14
• C32

Acknowledgments

The authors thank the Editor, Coeditor and two anonymous referees for helpful comments that significantly improve the article.

Additional information

Funding

The authors acknowledge partial research support from the Australian research council, and that from National Natural Science Foundation of China (Grant 71472007, 71532001 and 71671002), China’s National Key Research Special Program (2016YFC0207705), the Center for Statistical Science at Peking University, and Key Laboratory of Mathematical Economics and Quantitative Finance (Peking University), Ministry of Education.