Change points caused by extreme events in global economic markets have been widely studied in the literature. However, existing techniques to identify change points rely on subjective judgments and lack robust methodologies. The objective of this paper is to generalize a novel approach that leverages topological data analysis (TDA) to extract topological features from time series data using persistent homology. In this approach, we use Taken’s embedding and sliding window techniques to transform the initial time series data into a high-dimensional topological space. Then, in this topological space, persistent homology is used to extract topological features which can give important information related to change points. As a case study, we analyzed 26 stocks over the last 12 years by using this method and found that there were two financial market volatility indicators derived from our method, denoted as $L_1$ and $L_2$. They serve as effective indicators of long-term and short-term financial market fluctuations, respectively. Moreover, significant differences are observed across markets in different regions and sectors by using these indicators. By setting a significance threshold of 98 % for the two indicators, we found that the detected change points correspond exactly to four major financial extreme events in the past twelve years: the intensification of the European debt crisis in 2011, Brexit in 2016, the outbreak of the COVID-19 pandemic in 2020, and the energy crisis triggered by the Russia–Ukraine war in 2022. Furthermore, benchmark comparisons with established univariate and multivariate CPD methods confirm that the TDA-based indicators consistently achieve superior F1 scores across different tolerance windows, particularly in capturing widely recognized consensus events.

In live-streaming e-commerce systems, massive volumes of user-generated danmaku constitute a critical yet underutilized source of business intelligence. However, transforming such unstructured, noisy, and highly context-dependent textual data into structured and actionable knowledge remains a fundamental challenge for enterprise information systems. To address this issue, this study proposes TaSC-LLM, an LLM-enabled topic recognition method for constructing interpretable topic measurements from unstructured user-generated content. The proposed framework integrates topic taxonomy construction and zero-shot classification into a unified semantic reasoning pipeline. Unlike conventional topic modeling or supervised classification approaches, TaSC-LLM leverages chain-of-thought reasoning, multi-stage taxonomy induction, sliding window context modeling, and self-consistency verification to eliminate reliance on predefined label spaces and annotated training data. This design allows the system to dynamically construct and update topic taxonomies while ensuring interpretability, robustness, and cross-scenario adaptability. Empirical evaluation on three large-scale live-streaming e-commerce danmaku datasets shows that TaSC-LLM achieves strong taxonomy coverage, classification accuracy, and agreement with expert annotations. The findings suggest that LLM-based reasoning can help convert unstructured user-generated text into interpretable topic measures for downstream empirical and managerial analysis. While the present evaluation is conducted offline, TaSC-LLM provides a methodological foundation for future business applications that can be further examined under multi-session, multi-platform, and deployment-oriented conditions.