Cohomology theory for financial time series

Khovanov cohomology in time series data is used to model financial time in figure-eight hyperbolic knotted time series. We defined Chern–Simons current from the interaction of behavior of traders over Wilson loop with link eight states. We build a new path integral for the market phase transitions as Wilson loop between predictor and predictant paths in physiology of time series data. The obtained results are presented in the form of proved theorems. In the first theorem, we prove the existences of Chern–Simons current in the bid–ask spread as arbitrage opportunity for market phase transition of the interaction of Yang–Mills behavior field of the trader. In the second theorem, we prove the existence of market 8 states. As a consequence of the theorems, we classify the smallest subunit of market microstructure as 16 physiology cones according to all possibilities of the future outcome of endpoint state in time series data. The financial market movements for up and down directions with the curvature as link number are obtain from a market phase transition with eigenvalue of new defined Dirac operator for the financial market. The market curvature value appears as knot and link properties in time series data.