Multifractals and Fractional Brownian Motion

Papers:

• Mirowski -- From Mandelbrot to Chaos in Economic Theory

• Bacry, Delour, Muzy -- A multifractal Random Walk (2001)

• Bacry, Gloter, Hoffman, Muzy -- Multifractal Analysis in a Mixed Asymptotic Framework, 2008

• Bacry, Kozhemyak, Muzy, Continuous Cascade Models for Asset Returns, 2006

• Bacry, Kozhemyak, Muzy, Log Normal Continuous Cascades, Aggregation Properties and Estimation: Applications to Financial Time Series, 2008

• Baran -- Decision Making for Long Memory Data in Technical Economic Design, Fractals, and Decision Area Bubbles

• Borland, Bouchard, Muzy, Zumbach -- Mandelbrot's Multifractal Cascades and Beyond (2005)

• Ghorui -- A Simpler and Elegant Algorithm for Computing Fractal Dimension in Higher Dimensional State Space

• Mandelbrot -- A Multifractal Model of Asset Returns

• Mandelbrot -- Parallel Cartoons of Fractal Models of Finance, 2005

• Mansurov -- Forecasting Currency Crises by Fractal Analysis Techniques

• Mielniczuk and Wojdyllo -- Estimation of Hurst Exponent Revisited, 2007

• The Multifractal Model of Asset Return Versus Real Stock Market Dynamics

• Mulligan -- A fractal analysis of foreign exchange markets

• Muzy, Bacry, and Kozhemyak -- Extreme Values and Fat Tails of Multifractal Fluctuations, 2005

• Sun -- Fractals in Trade Duration: Capturing Long Range Dependence and Heavy Tailedness in Modeling Trade Duration

  • Constantine and Percival, Wavelet Based Analysis and Software for Multiscale Fractal Processes, 2002

Books:

• Mandelbrot and Hudson, 2004, The (Mis)Behavior of Markets

• Fractal Market Analysis

Other:

• http://sage.math.washington.edu/home/simuw/simuw08/refs/fractal/