Identifying and Forecasting Recurrently Emerging Stock Trend Structures via Rising Visibility Graphs

This study introduces a novel forecasting framework that identifies and predicts recurrently emerging structural patterns in stock trends using rising visibility graphs (RVGs) and the Weisfeiler–Lehman (WL) subtree kernel. The proposed method, RVGWL, addresses a key limitation of traditional visibility graphs, namely the structural indistinguishability between rising and falling trends, by selectively constructing edges only along upward price movements. This approach produces graph representations that capture direction-sensitive market dynamics and facilitate the extraction of meaningful topological features from price data. By applying the WL kernel, RVGWL quantifies structural similarities between graph-transformed time series, enabling the identification of structurally similar preceding patterns and the probabilistic forecasting of their subsequent trajectories based on nine canonical trend templates. Experiments on time series data from four major stock indices and their constituent stocks during the year 2023—characterized by diverse market regimes across the U.S., Japan, the U.K., and China—demonstrate that RVGWL consistently outperforms classical rule-based strategies. These results support the predictive value of recurring topological structures in financial time series and higight the potential of structure-aware forecasting methods in quantitative analysis.