Figure 1.

The time series multifractal (upper panel), monofractal (middle panel), and whitenoise (lower panel) are shown as blue traces. They are examples of noise like time series used in the present tutorial. All time series contain 8000 data samples each where the sample numbers are indicated by the horizontal axis. Matlab code 1 converts the noises (blue traces) to random walks (red traces) that have a picture-in-picture similarity (subplot in the upper panel). Notice that the time series multifractal has distinct periods with small and large fluctuations in contrast to time series monofractal and whitenoise. The aim of this section is to introduce MFDFA that quantify the structure of fluctuations within the periods with small and large fluctuations.