Topological Compression of Belief States in Prediction Markets for Event Forecasting

This study introduces topological data analysis (TDA) and persistent homology (PH) into forecasting models in the field of prediction markets, exploring whether the underlying structure of market belief states has predictive value. The research findings show that single-parameter PH can improve the predictive power and calibration accuracy of linear forecasting models, and that two-parameter multi-persistent homology can produce similar gains for nonlinear models. The paper is 41 pages long with 19 figures, and belongs to the field of Trading and Market Microstructure (q-fin.TR).