GARCH in spinor field

Abstract

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 [Formula: see text], 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 [Formula: see text], the so-called modeling of the financial market in icosahedral supersymmetry gauge group.