  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.
