Title: A self-exciting threshold autoregressive count data model
Authors: Namhyun Kim - University of Exeter (United Kingdom) [presenting]
Abstract: A new approach to modelling nonlinear time series of counts is proposed. In particular, the aims is to provide an instantaneous prediction of counts showing highly nonlinear phenomena such as limit cycles, jump resonance, harmonic distortion, modulation effects and chaos. Although the simple and intuitive benefits of using a Poisson process are well-known, the alternative, a Type II negative binomial (NB) process. The NB process provides a convenient way of introducing any type of serial dependence into counts by mixing a Poisson with a Gamma processes in which the dynamic evolution of counts is driven by the conditional mean. The conditional mean is specified with the well-known self-exciting threshold type of the process to describe the above nonlinearities in dynamic counts. The intrinsic presence of the latent stochastic conditional mean in the proposed likelihood motivates us to represent the proposed process with a legitimate linear state-space model by introducing a tuning parameter. Hence, the well-known linear filter is applied then the unknown parameters in the proposed process are estimated via quasi maximum likelihood estimation. The asymptotic properties of the proposed QMLEs are also studied and their finite sample performances are shown with Monte Carlo designs.