Generalized varying-coefficient additive model for locally stationary time series

ABSTRACT

Recently, the varying-coefficient additive model (VCAM) has received much attention due to its flexibility and interpretability. In this paper, we consider its generalized form, called a generalized varying-coefficient additive model (GVCAM), which can model discrete and continuous responses for locally stationary covariates. Specifically, the conditional mean function is specified via a link function g and a nonparametric part given by a VCAM. We develop a pilot-estimation-based local linear maximum likelihood estimator (PEB-LLE) to approximate the univariate component function. We also show the proposed estimators are oracle efficient and present the pointwise asymptotic distribution as well as simultaneous confidence bands. Simulation studies investigating the finite-sample performance of the proposed methodology are considered, and a real data application illustrating our method is also given.

KEYWORDS:

• Generalized varying-coefficient additive model
• maximum likelihood estimation
• locally stationary

Acknowledgements

The authors are grateful to an associate editor and referees for their constructive comments that have substantially improved the quality of this article.

Disclosure statement

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

Additional information

Funding

This work was supported by National Social Science Founds of China [No. 21BTJ039]; National Social Science Fund of China [No. 19BTJ032].