Marginal likelihood estimation for the negative binomial INGARCH model

Abstract

In recent years, there has been increased interest in modeling integer-valued time series. Many methods for time series of counts have been developed in the literature because of their wide applications to epidemiology, finance, disease modeling and environmental science. The negative binomial integer-valued generalized autoregressive conditional heteroscedasticity model is a popular one, which can deal with both over-dispersion and potential extreme observations. The accurate estimation of the parameters in the model is extremely important. We adopt the marginal likelihood to estimate the intercept parameter and maximum likelihood to estimate other parameters of the model. We conduct simulations to assess the performance of this estimation method, and compare it with that of estimating all model parameters by maximum likelihood. The results show the superiority of proposed estimation method. We use two real examples to illustrate the model’s ability to fit over-dispersed data and the validity of the estimation method.