Multifractal regime transition in a modified minority game model

TL;DR

This paper demonstrates that a modified minority game model exhibits multifractal properties in its price signals, providing a more realistic representation of financial market dynamics.

Contribution

It introduces a variant of the Minority Game model that displays multifractality, unlike the standard version, enhancing its realism for financial modeling.

Findings

The nonsynchronous MG model in the nonergodic phase is multifractal.

The model's multifractal spectrum varies across different dynamical regimes.

The structure function and WTMM methods effectively characterize the multifractal properties.

Abstract

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual Minority Game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the Structure Function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (nonlinear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the Wavelet Transform Modulus Maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes.