Uniform consistency for local fitting of time series non-parametric regression allowing for discrete-valued response

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 β-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 © 2022 American Psychological Association