Weighted empirical likelihood inferences for a class of varying coefficient ARCH-M models

Abstract

In this paper, we consider the empirical likelihood inferences for a class of varying coefficient ARCH-M models, which is an extended version of parametric ARCH-M models. By constructing a weighted auxiliary random vector, we propose a weighted empirical likelihood method for estimating the functional-coefficients. Under some regularity conditions, the constructed empirical log-likelihood ratio is shown to be asymptotically ${\chi }^2$, and then the pointwise confidence interval for functional-coefficient is constructed. Some simulation studies are carried out to compare finite sample performances of the proposed empirical likelihood estimation method with some existing estimation methods under various model settings. A real data analysis is also undertaken to illustrate practical implementation and performance of the proposed estimation procedure.

Keywords:

• Varying coefficient model
• ARCH-M model
• weighted empirical likelihood
• confidence interval

2010 Mathematics Subject Classifications:

• 62G05
• 62G20
• 62G30

Acknowledgments

We thank the reviewers, the associated editor and the editor if chief, whose comments have led to many improvements in this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is supported by the National Social Science Foundation of China [grant number 18BTJ035], the Natural Science Foundation of Chongqing [grant number cstc2020jcyj-msxmX0006], and the Natural Science Foundation of Shandong [grant number ZR2020MA021].