Statistics and Its Interface
Volume 16 (2023)
Special issue on recent developments in complex time series analysis – Part II
Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)
Uniform consistency for local fitting of time series non-parametric regression allowing for discrete-valued response
Pages: 305 – 318
Local linear kernel fitting is a popular nonparametric technique for modelling nonlinear time series data. Investigations into it, although extensively made for continuousvalued case, are still rare for the time series that are discrete-valued. In this paper, we propose and develop the uniform consistency of local linear maximum likelihood (LLML) fitting for time series regression allowing response to be discrete-valued under $\beta$-mixing dependence condition. Specifically, the uniform consistency of LLML estimators is established under time series conditional exponential family distributions with aid of a beta-mixing empirical process through local estimating equations. The rate of convergence is also provided under mild conditions. Performances of the proposed method are demonstrated by a Monte-Carlo simulation study and an application to COVID-19 data. There is a huge potential for the developed theory contributing to further development of discrete-valued response semiparametric time series models.
uniform consistency, discrete-valued time series, exponential family, local linear fitting, $\beta$-mixing, non-parametric
2010 Mathematics Subject Classification
Primary 62M10, 62M20. Secondary 62G05.
Received 31 May 2021
Accepted 13 June 2022
Published 13 April 2023