DETECTING MULTIFRACTAL PROPERTIES IN ASSET RETURNS: THE FAILURE OF THE "SCALING ESTIMATOR"

摘要: It has become popular recently to apply the multifractal formalism of statistical physics (scaling analysis structure functions and f(α) singularity spectrum analysis) financial data. The outcome such studies is a nonlinear shape function nontrivial behavior spectrum. Eventually, this literature moved from basic data estimation particular variants models for asset returns via fitting empirical τ(q) functions. Here, we reinvestigate earlier claims multifractality using four long time series important markets. Taking proposed as our starting point, show that typical "scaling estimators" used in are unable distinguish between spurious "true" multiscaling Designing explicit tests multiscaling, can no case reject null hypothesis apparent curvature both scaling Holder spuriously generated by fat-tailed distribution Given well-known overwhelming evidence favor different degrees long-term dependence powers returns, interpret inability lack discriminatory power standard approach rather than true rejection multiscaling. However, complete "failure" apparatus setting also raises question whether results other areas (like geophysics) suffer similar shortcomings traditional methodology.