Fuzzy Jump Models for Soft and Hard Clustering of Multivariate Time Series Data
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多变量时间序列软聚类与硬聚类的模糊跳跃模型
- 研究问题
- 时间序列状态具有持续性但归属不确定时，如何在抑制频繁状态切换的同时刻画软归属，并兼容多变量混合类型数据？
- 方法与思路
- 作者结合统计跳跃模型与模糊 c 均值框架，序贯估计时变状态概率，通过模糊参数调节软聚类与硬聚类。
- 材料陈述的贡献
- 摘要称在高归属不确定性的模拟中优于比较方法，并在三体问题和五类金融资产数据中展示持续状态识别能力。
- 阅读关注点
- 核对聚类目标、跳跃惩罚及模糊参数的选择，状态概率的解释，以及潜在状态恢复与金融牛熊识别的评价基准。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未给出调参规则及误差数值，聚类状态也未获因果解释。
原文摘要
Statistical jump models have been recently introduced to detect persistent regimes by clustering temporal features and discouraging frequent regime changes. However, they are limited to hard clustering and thereby do not account for uncertainty in state assignments. This work presents an extension of the statistical jump model that incorporates uncertainty estimation in cluster membership. Leveraging the similarities between statistical jump models and the fuzzy c-means framework, our fuzzy jump model sequentially estimates time-varying state probabilities. Our approach offers high flexibility, as it supports both soft and hard clustering through the tuning of a fuzziness parameter, and it naturally accommodates multivariate time series data of mixed types. Through a simulation study, we evaluate the ability of the proposed model to accurately estimate the true latent-state distribution, demonstrating that it outperforms competing approaches under high cluster assignment uncertainty. We further demonstrate its utility on two empirical applications: first, by automatically identifying co-orbital regimes in the three-body problem, a novel application with important implications for understanding asteroid behavior and designing interplanetary mission trajectories; and second, on a financial dataset of five assets representing distinct market sectors (equities, bonds, foreign exchange, cryptocurrencies, and utilities), where the model accurately tracks both bull and bear market phases.