Topological analysis of time series and their relation to stock market data

Sammanfattning

This Bachelor's thesis investigates whether topological data analysis can identify correlations between weather patterns and stock market movements. The primary objective was to apply a topological pipeline to weather data to determine if hidden geometrical structures correlate with financial market behavior. Hourly weather data was collected from five Swedish stations between January 1, 2024, and December 31, 2025. The analytical pipeline uses a combination of Takens's embedding theorem and a sliding window technique, followed by an analysis using persistent homology. To compare the topological features with stock market data, a cross-correlation analysis was performed with time shifts of up to 30 days. The results revealed a negligible overall correlation across all lags. Although minor correlation peaks occurred at a 30-day lag for both wind and precipitation, the findings suggest that any potential interaction is likely delayed rather than immediate, and ultimately weak.