A novel time‐varying coefficient Poisson difference model driven by observation

Abstract

This paper studies a novel time‐varying coefficient integer‐valued time series model driven by observation. The model is suitable for modeling negative integer‐valued time series based on the Poisson difference distribution and extended binomial thinning operator. Main methods used to estimate the parameters are the conditional least squares (CLS) and conditional maximum likelihood (CML) methods. This paper also discusses the consistency and asymptotic normality of the estimation results. Likelihood ratio tests are employed to examine the existence of covariate and observation. Numerical simulations are conducted to verify the accuracy and stability of the model. Finally, a real data application is presented to demonstrate the usefulness and adaptability of this newly proposed model.