Multifractal regime transition in a modified minority game model

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.

Identifying financial crises in real time

“…To address these problems we shall use multifractal techniques known to capture non trivial scale properties as shown by Mandelbrot (a pioneer to find self-similarity in the cotton prices distribution [1,2]); by Evertsz [3], who confirmed the distributional self-similarity and suggested that market self-organizes to produce such feature also; by Mantegna and Stanley [4], who found a power law scaling behavior over three orders of magnitude in the S&P 500 index variation. These works were an important hallmark to shed light in the financial market dynamics [5]. It shows that we can use concepts and tools from statistical mechanics to model and analyze financial data [6,7,8,9,10,11,12,13].…”

Delayed Majority Game with Heterogeneous Learning Speeds for Financial Markets

“…Here we introduce two previous artificial markets which focus on heterogeneity of agents; in Ref. [17], the model reconstructs volatility clustering by considering the heterogeneity of the decision making and Ref [18] is an examples of minority games with heterogeneity.…”

Pointwise Regularity Exponents and Well-Behaved Residuals in Stock Markets

“…An idea of how estimator (8) works is provided in Figure 6: panel (a) displays a trajectory of Z(t, ω) with its increments; panel (b) shows the functional parameter ( , ) t ω H and panel (c) the absolute error of the estimates provided by Once the estimation of H(t,ω) was obtained through (8), we used it to calculate the residuals in the usual way…”

“…Estimator defined by (8): assumes the increments process X j+q,n -X j,n to be normally distributed within the window δ with mean zero and Figure 6. Sample autocorrelation function of the MPRE variance given by relation (5).…”

“…From a practitioner viewpoint, many reasons justify the use of the MPRE as a model of the financial dynamics; detailed discussions can be found in [5], [6], [7], [8] and [9]. Here we restrict ourselves to mention the capability the process has to (a) provide a rationale for the trading Pointwise Regularity Exponents and Well-Behaved Residuals in Stock Markets Sergio Bianchi and Alexandre Pantanella mechanism, and (b) replicate the stylized facts observed in finance.…”