讲座题目：Unified Approaches to White Noise Testing: Bridging Time, Frequency, and Functional Domains
内容摘要：This lecture presents a unified framework for white noise and diagnostic checking in time series analysis, tracing its methodological evolution from the time domain to the frequency domain and from finite-dimensional Euclidean spaces to infinite-dimensional Hilbert spaces.
Starting from the time-domain portmanteau framework for weak vector autoregressive models, we show that conventional test statistics often suffer from substantial size distortions due to unknown error dependence structures and parameter estimation effects. To overcome these limitations, we develop a blockwise random-weighting bootstrap procedure, which accurately approximates the null distribution and its asymptotic validity is justified. Extending this idea to the frequency domain，a Cramér–von Mises type statistic is constructed based on the discrepancy between the residual periodogram and its theoretical constant, enabling the detection of long-range dependence beyond finite lags while maintaining robustness to estimation uncertainty. Finally, the framework is generalized to functional time series in a Hilbert space setting, where portmanteau-type statistics based on squared empirical autocorrelation operators are employed to assess functional white noise and model adequacy.
Collectively, these developments provide a coherent and theoretically justified approach that robustly mitigates the impact of unknown dependence and estimation uncertainty in time series models.
主讲人简介：李木易，香港大学统计学博士，现任厦门大学 WISE 与经济学院统计学与数据科学系双聘教授、博士生导师、系副主任。主要研究方向为非线性时间序列、金融计量、模型检验等。论文发表于Journal of Econometrics, Journal of Business and Economic Statistics，Journal of Time Series Analysis, Statistica Sinica等国际权威期刊。主持完成国家自然科学基金项目3项、以及全国统计科学研究重点项目、福建省基金项目、教育部计量经济学重点实验室实验教学项目等。参与国家自然科学基金重点项目“经济大数据的宏观计量建模: 理论、方法和应用”（在研）。主讲中国大学慕课《时间序列分析》（已开设8轮次）。获得福建省教学成果特等奖（2022，团体）、国家级教学成果二等奖（2023，团体）。获得“厦门大学我最喜爱的十位老师”称号（2025）。
报告时间：2025年10月28日(周二)，16:30-18:00
线下地点：厦门大学经济楼C108
线上地点：腾讯会议 ID：379 729 547
