Speaker: ZHU Fukang, Professor, School of Mathematics, Jilin University
Venue: Tencent meeting ID: 788 902 078
Abstract:
During the last decades, a large variety of models have been proposed for count time series, where the integer-valued autoregressive moving average (ARMA) and integer-valued generalized autoregressive conditional heteroskedasticity (INGARCH) models are the most popular ones. However, while both models lead to an ARMA-like autocorrelation function (ACF), the attainable range of ACF values is much more restricted and negative ACF values are usually not possible. The existing log-linear INGARCH model allows for negative ACF values, but the linear conditional mean and the ARMA-like autocorrelation structure are lost. To resolve this dilemma, a novel family of INGARCH models is proposed, which uses the softplus function as a response function. The softplus function behaves approximately linear, but avoids the drawback of not being differentiable in zero. Stochastic properties of the novel model are derived. The proposed model indeed exhibits an approximately linear structure, which is confirmed by extensive simulations, and which makes its model parameters easier to interpret than those of a log-linear INGARCH model. The asymptotics of the maximum likelihood estimators for the parameters are established, and their finite-sample performance is analyzed via simulations. The usefulness of the proposed model is demonstrated by applying it to three real-data examples.