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Cohomology theory for financial time series

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  • Kanjamapornkul, Kabin
  • Pinčák, Richard
  • Bartoš, Erik

Abstract

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.

Suggested Citation

  • Kanjamapornkul, Kabin & Pinčák, Richard & Bartoš, Erik, 2020. "Cohomology theory for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 546(C).
    • Handle: RePEc:eee:phsmap:v:546:y:2020:i:c:s037843711931283x
    DOI: 10.1016/j.physa.2019.122212
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    References listed on IDEAS

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    1. Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623, arXiv.org.
    2. Ochiai, Tomoshiro & Nacher, Jose C., 2014. "Volatility-constrained correlation identifies the directionality of the influence between Japan’s Nikkei 225 and other financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 364-375.
    3. Richard Pincak & Kabin Kanjamapornkul, 2018. "GARCH(1,1) model of the financial market with the Minkowski metric," Papers 1808.04231, arXiv.org.
    4. Kabin Kanjamapornkul & Richard Pinv{c}'ak & Sanphet Chunithpaisan & Erik Bartov{s}, 2017. "Support Spinor Machine," Papers 1709.03943, arXiv.org.
    5. Robert Engle, 2004. "Risk and Volatility: Econometric Models and Financial Practice," American Economic Review, American Economic Association, vol. 94(3), pages 405-420, June.
    6. Schoder, Christian, 2017. "Are Dynamic Stochastic Disequilibrium models Keynesian or neoclassical?," Structural Change and Economic Dynamics, Elsevier, vol. 40(C), pages 46-63.
    7. Kanjamapornkul, K. & Pinčák, Richard & Bartoš, Erik, 2016. "The study of Thai stock market across the 2008 financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 117-133.
    8. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    9. Goldstein, Michael A. & A. Kavajecz, Kenneth, 2000. "Eighths, sixteenths, and market depth: changes in tick size and liquidity provision on the NYSE," Journal of Financial Economics, Elsevier, vol. 56(1), pages 125-149, April.
    10. K. Kanjamapornkul & R. Pinv{c}'ak, 2016. "Kolmogorov Space in Time Series Data," Papers 1606.03901, arXiv.org.
    11. Christian Schoder, 2017. "An estimated Dynamic Stochastic Disequilibrium model of Euro-Area unemployment," Working Papers 1725, New School for Social Research, Department of Economics.
    12. Bartoš, Erik & Pinčák, Richard, 2017. "Identification of market trends with string and D2-brane maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 57-70.
    13. Mark Buchanan, 2009. "Economics: Meltdown modelling," Nature, Nature, vol. 460(7256), pages 680-682, August.
    14. Garman, Mark B., 1976. "Market microstructure," Journal of Financial Economics, Elsevier, vol. 3(3), pages 257-275, June.
    15. Simone Farinelli, 2009. "Geometric Arbitrage Theory and Market Dynamics Reloaded," Papers 0910.1671, arXiv.org, revised Jul 2021.
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