Multivariate multifractal analysis

A multivariate multifractal model for return fluctuations

In this paper we briefly review the recently inrtroduced Multifractal Random Walk (MRW) that is able to reproduce most of recent empirical findings concerning financial time-series : no correlation between price variations, long-range volatility correlations and multifractal statistics. We then focus on its extension to a multivariate context in order to model portfolio behavior. Empirical esti...

Multifractal analysis for all

Multifractal formalism and analysis have been described many times (Lopes and Betrouni, 2009). There are several approaches to the implementation of multifractal analysis and there numerous ways to present these (Olsen, 1995; Wendt et al., 2009; Ihlen, 2012). Ihlen’s article, in the June 4th 2012 issue of Frontiers of Physiology, entitled “Introduction to multifractal detrended fluctuation anal...

Box-counting multifractal analysis.

Local Multifractal Analysis

We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out several examples of measures and functions where this setting is relevant.

Multifractal Analysis of Hyperbolic Flows

We establish the multifractal analysis of hyperbolic flows and of suspension flows over subshifts of finite type. A non-trivial consequence of our results is that for every Hölder continuous function noncohomologous to a constant, the set of points without Birkhoff average has full topological entropy.