摘要：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.
简历：朱复康，吉林大学数学学院教授、博士生导师，概率统计与数据科学系主任。2008年博士毕业，2013年被聘为教授。主要从事时间序列分析和金融统计的研究，已经在Annals of Applied Statistics、Statistica Sinica、Journal of Time Series Analysis等杂志上发表论文40余篇，被他人引用490余次，单篇文章最高引用110余次。作为负责人获得省部级以上科研项目9项，其中国家自然科学基金4项。现任中国数学会概率统计学会、中国现场统计研究会等学会的理事或常务理事，美国数学会《数学评论》评论员，已经为JRSSB、JBES等50余个杂志审稿100余次。