Functional Spectral Analysis for Time Series Classification

：陈坤（西南财经大学）
：2026-03-12 16:30
：海韵园行政楼C503

报告人：陈坤（西南财经大学）

时  间：2026年3月12日16:30

地  点：海韵园行政楼C503

内容摘要:

Traditional spectral classification methods for stationary time series typically characterize differences based on vectors of periodogram ordinates, or their logarithms, evaluated at discrete frequencies. However, these estimators often fail to leverage the intrinsic smoothness of the underlying (log-)spectral density function. This paper proposes a novel Spectral Functional Classification (SFC) procedure that addresses this limitation by treating the smoothed log-periodogram as a functional object. Specifically, by employing Functional Principal Component Analysis, the procedure extracts the most important components of the spectral density and achieves a significant denoising effect by filtering out stochastic noise. We further introduce a data-driven procedure for selecting the optimal number of principal components. Under mild conditions, we establish the consistency of our estimators and provide a rigorous proof of classification consistency, demonstrating that the misclassification probability vanishes in the double-asymptotic regime (as both the number of time series n and the series length T approach infinity). Extensive simulations and a real data application demonstrate the superior accuracy and robustness of the SFC approach compared to existing methods.

个人简介：

陈坤，西南财经大学统计学院教授、博士生导师，光华英才学者，研究方向为时间序列分析、空间统计、函数型数据分析和金融统计。担任国家一流课程负责人。荣获光华优秀硕士学位论文指导教师。多次指导学生获得统计建模比赛国家级奖项。曾多次赴日本早稻田大学、香港城市大学、浙江大学和其他国内外多所高校访问。为香港城市大学统计学研究生开设课程。主持并参与了多项国家社会科学基金、国家自然科学基金项目、教育部人文社科项目；在《Annals of Statistics》等国内外重要期刊发表论文；是《Journal of the American Statistical Association》、《Statistica Sinica》、《Bernoulli》、《Journal of Time Series Analysis》等多个期刊的匿名审稿人。

 

联系人：胡杰