Empirical likelihood-based unified confidence region for a predictive regression model

Abstract

In finance and economics, predictive regression models are widely used. It is known that the limit distributions of their least squares estimators are nonstandard, and depend on the properties of the predictors. In this paper, we consider the unified confidence region construction of a predictive regression model by using empirical likelihood. It turns out that the resulting statistic has an asymptotical chi-squared distribution regardless of the predictor being stationary or non-stationary. Simulations are also conducted to illustrate its finite sample performance.

Keywords:

• Predictive regression model
• Empirical likelihood
• Unified confidence region

Acknowledgments

We thank Professor Liang Peng for simulating this research. Our thanks also go to the reviewer’s comments, which have led to many improvements in this paper.

Additional information

Funding

Xiaohui Liu’s research is supported by NSF of China (Grant Nos. 11971208 and 11601197), China Postdoctoral Science Foundation funded project (2016M600511 and 2017T100475), the Postdoctoral Research Project of Jiangxi (No. 2017KY10), NSF of Jiangxi Province (Nos. 2018ACB21002 and 20171ACB21030). Yuzi Liu’s research is partly supported by the Postgraduate Innovation Project of Jiangxi Province (Nos. YC2019-S216 and xskt19393). Fucai Lu’s research is supported by NSF of China (Nos. 71863015 and 71463020).