Academic Report of the School of Mathematical Sciences [2025] No. 095  

(High-Level University Construction Series Report No. 1117)  

Lecture Title: Mean-preserving rounding integer-valued time series models  

Lecturer: Professor Zhu Fukang (Jilin University)  

Lecture Time: October 14, 2025, 15:00-16:00 (afternoon)  

Venue: Conference Room 303, Alumni Plaza, Yuehai Campus, Shenzhen University  

Abstract:  

In the past four decades, research on count time series has made significant progress, but research on Z-valued time series is relatively rare. Existing Z-valued models are mainly of autoregressive structure, where the use of the rounding operator is very natural. Because of the discontinuity of the rounding operator, the formulation of the corresponding model identifiability conditions and the computation of parameter estimators need special attention. It is also difficult to derive closed-form formulae for crucial stochastic properties. We rediscover a stochastic rounding operator, referred to as mean-preserving rounding, which overcomes the above drawbacks. Then, a novel class of Z-valued ARMA models and its vector version based on the new operator is proposed, and the existence of stationary solutions of the models is established. Stochastic properties are obtained. The advantages of our novel model class compared to existing ones are demonstrated. In particular, our model construction avoids identifiability issues such that maximum likelihood estimation is possible.

Lecturer’s Biography:  

Zhu Fukang is a Professor and Doctoral Supervisor at the School of Mathematics, Jilin University. He also serves as Deputy Director of the Jilin National Center for Applied Mathematics and Director of the Department of Probability, Statistics and Data Science. He received his doctoral degree in 2008 and was exceptionally promoted to Professor in 2013. His main research focuses on time series analysis and financial statistics. He has published numerous papers in journals such as Annals of Applied Statistics, Journal of Business & Economic Statistics, Statistica Sinica, Scandinavian Journal of Statistics, Journal of Time Series Analysis, and Science China - Mathematics. He has presided over 3 General Programs and 1 Youth Program of the National Natural Science Foundation of China. He has received multiple awards, including the Second Prize of the Natural Science Award of the Ministry of Education, the Second Prize of the Jilin Provincial Science and Technology Award, the title of "Expert Enjoying Government Allowance of Jilin Province," and "Expert with Outstanding Contributions of Changchun City." He has been included in Stanford University’s "World's Top 2% Scientists List" for three consecutive years (2023-2025).  

Currently, he holds positions as Director or Standing Director of societies including the Chinese Association of Applied Statistics, the National Teaching Research Association of Industrial Statistics, and the Probability and Statistics Branch of the Chinese Mathematical Society. He also serves as Associate Editor of the SCI-indexed journals Statistical Papers and Journal of Statistical Computation and Simulation, and acts as an anonymous reviewer for over 80 SCI-indexed journals such as JASA, JRSSB, JBES, and AoAS. Among the postgraduates he supervised, one has won the Jilin Provincial Excellent Doctoral Dissertation, and three have won the Jilin Provincial Excellent Master's Dissertation.  

Faculty and students are welcome to attend!  

Inviter: Zhou Yan  

School of Mathematical Sciences  

October 11, 2025