A Brief Overview of Multifractal Time Series

In the Exploring Patterns in Nature tutorials, we observed how disordered, irregular, fractal patterns can be quantified in terms of their spatial fractal dimension. Here we study fractal (and multifractal) patterns of a different sort: patterns in time.

This overview attempts to give a short operational review of multifractality in time series. For this reason, formal definitions and derivations are not discussed; see Refs. 1-4 for more in-depth reviews.

• Part 1: Fractal behavior in time series
• Part 2: Using wavelets to detect singular behavior
• Part 3: The fractal dimension of the singular behavior
• Part 4: The singularity spectra of multifractal signals
• Part 5: What one learns from the singularity spectra of multifractal signals
• Part 6: Multifractality of healthy human heart rate
• Bibliography

Software for multifractal analysis of time series is available here.