报告时间：2025年8月21号 16：30-17：30

报告地点：统计与数据科学学院106

报告题目：Tobit models for count time series

报告摘要：Several models for count time series have been developed during the last decades, often inspired by traditional autoregressive moving average (ARMA) models for real-valued time series, including integer-valued ARMA (INARMA) and integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models. Both INARMA and INGARCH models exhibit an ARMA-like autocorrelation function (ACF). To achieve negative ACF values within the class of INGARCH models, log and softplus link functions are suggested in the literature, where the softplus approach leads to conditional linearity in good approximation. However, the softplus approach is limited to the INGARCH family for unbounded counts, i.e., it can neither be used for bounded counts, nor for count processes from the INARMA family. In this paper, we present an alternative solution, named the Tobit approach, for achieving approximate linearity together with negative ACF values, which is more generally applicable than the softplus approach. A Skellam--Tobit INGARCH model for unbounded counts is studied in detail, including stationarity, approximate computation of moments, maximum likelihood and censored least absolute deviations estimation for unknown parameters and corresponding simulations. Extensions of the Tobit approach to other situations are also discussed, including underlying discrete distributions, INAR models, and bounded counts. Three real-data examples are considered to illustrate the usefulness of the new approach.

报告人简介：朱复康，吉林大学数学学院教授、博士生导师，吉林国家应用数学中心副主任、概率统计与数据科学系主任。2008年博士毕业，2013年破格晋升教授，2021年任唐敖庆领军教授。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、Journal of Business & Economic Statistics、Statistica Sinica、Scandinavian Journal of Statistics、Journal of the Royal Statistical Society Series A、Journal of Time Series Analysis、中国科学-数学等期刊上发表论文多篇，主持国家自然科学基金面上项目3项和青年基金1项。曾获教育部自然科学奖二等奖、吉林省科学技术奖二等奖、吉林省享受省政府津贴专家、长春市有突出贡献专家等奖励，连续两年(2023-2024)入选美国斯坦福大学发布的全球前2%顶尖科学家榜单。现任中国现场统计研究会、全国工业统计学教学研究会、中国数学会概率统计分会等学会的理事或常务理事。现任SCI期刊Statistical Papers、Journal of Statistical Computation and Simulation的副主编，是JASA、JRSSB、JBES、AoAS等80余个SCI期刊的匿名审稿人。指导的研究生1人获得吉林省优秀博士学位论文、3人获得吉林省优秀硕士学位论文。