Double Dynamic Bounded Full-integer-valued Garch Model

This article introduces a novel double dynamic trinomial GARCH model with the simultaneous modeling of the time-varying mean and variance to analyze bounded full-integer-valued time series.In this paper, we construct a trinomial autoregressive process to analyze zero-mean process with time-varying variance process, and then propose a novel double dynamic trinomial autoregressive process to analyze non-zero and time-varying mean process, besides the time-varying variance process.Furthermore, we discuss their stationarity and ergodicity, give the conditional maximum likelihood estimate, and derive their asymptotic properties.We also provide details on one-step-ahead forecasting.The performances of these estimators are compared via simulation study.Finally, we apply the proposed model to two datasets to demonstrate its favorable performance.