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GARCH in spinor field. (English) Zbl 1425.91437

Summary: We extend generalized autoregressive conditional heteroscedastic (GARCH) errors in the Euclidean plane of the scalar field to the tensor field and to the spinor field \(\text{HP}^1\), the so-called spinor garch, S-GARCH. We use the model of S-GARCH to explain the stylized fact in financial time series, the so-called volatility cluster, by using hyperbolic coordinate with induced complex lag of delay time scale in mirror symmetry concept. As the result of this theory, we obtain an equivalent form of Yang-Mills equation for financial time series as the interaction between the behavior of traders, the so-called, fundamentalist, chatlist and noise trader, by using volatility in spinor field with invariant of the gauge group \(\text{SO}(3 2)\), the so-called modeling of the financial market in icosahedral supersymmetry gauge group.

MSC:

91G80 Financial applications of other theories
62P05 Applications of statistics to actuarial sciences and financial mathematics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
81T13 Yang-Mills and other gauge theories in quantum field theory
81R25 Spinor and twistor methods applied to problems in quantum theory
81T60 Supersymmetric field theories in quantum mechanics
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