7.2 Multi-fractal DFA

casnet has a function for multi-fractal DFA based on the Matlab code by E.A.F. Ihlen: Introduction to multifractal detrended fluctuation analysis in Matlab

set.seed(33)

# White noise
fd_mfdfa(rnorm(4096), doPlot = TRUE)

> 
> 
> (mf)dfa:  Sample rate was set to 1.

> 
> ~~~o~~o~~casnet~~o~~o~~~
> 
>  Multifractal Detrended FLuctuation Analysis 
> 
>   Spec_AUC Spec_Width Spec_CVplus Spec_CVmin Spec_CVtot Spec_CVasymm
> 1   0.0977      0.104      0.0495     0.0513     0.0503      -0.0179
> 
> 
> ~~~o~~o~~casnet~~o~~o~~~

# Pink noise
fd_mfdfa(noise_powerlaw(N=4096), doPlot = TRUE)

> 
> 
> (mf)dfa:  Sample rate was set to 1.

> 
> ~~~o~~o~~casnet~~o~~o~~~
> 
>  Multifractal Detrended FLuctuation Analysis 
> 
>   Spec_AUC Spec_Width Spec_CVplus Spec_CVmin Spec_CVtot Spec_CVasymm
> 1    0.284      0.328       0.085      0.198      0.155       -0.399
> 
> 
> ~~~o~~o~~casnet~~o~~o~~~

# 'multi' fractal
N <- 2048
y <- rowSums(data.frame(elascer(noise_powerlaw(N=N, alpha = -2)), elascer(noise_powerlaw(N=N, alpha = -.5))*c(rep(.2,512),rep(.5,512),rep(.7,512),rep(1,512))))
fd_mfdfa(y=y, doPlot = TRUE)

> 
> 
> (mf)dfa:  Sample rate was set to 1.

> 
> ~~~o~~o~~casnet~~o~~o~~~
> 
>  Multifractal Detrended FLuctuation Analysis 
> 
>   Spec_AUC Spec_Width Spec_CVplus Spec_CVmin Spec_CVtot Spec_CVasymm
> 1     0.14      0.169       0.031      0.179      0.145       -0.705
> 
> 
> ~~~o~~o~~casnet~~o~~o~~~