MMA {MFDFA}

Multiscale Multifractal Analysis

Description

Applies the Multiscale Multifractal Analysis (MMA) on time series.

Usage

MMA(tsx, scale, qminmax, ovlap=0, m=2)

Arguments

tsx

Univariate time series (must be a vector or a ts object).

scale

Vector of scales.

qminmax

Vector of two values min and max of q-order of the moment.

ovlap

Overlapping parameter (By default ovlap=0: no overlapping).

m

Polynomial order for the detrending (by defaults m=2).

Value

A matrix with three columns (q-order, scale (s), and the scale exponent).

Note

The original code of this function is in Matlab, you can find it on the following website Physionet. See references below.

References

J. Feder, Fractals, Plenum Press, New York, NY, USA, 1988.

J. Gieraltowski, J. J. Zebrowski, and R. Baranowski, Multiscale multifractal analysis of heart rate variability recordings http://dx.doi.org/10.1103/PhysRevE.85.021915

Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh, Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101(23):e215-e220.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A: Statistical Mechanics and its Applications, 316 (1) (2002) 87 – 114.

J. Gierałtowski, J. J. Żebrowski, and R. Baranowski, "Multiscale multifractal analysis of heart rate variability recordings with a large number of occurrences of arrhythmia," Phys. Rev. E 85, 021915 (2012)

Examples

## Not run: 
library(MFDFA)
library(plotly)
library(plot3D)

a<-0.6
N<-800
tsx<-MFsim(N,a)
scale=10:100
res<-MMA(tsx, scale, qminmax=c(-10,10), ovlap=0, m=2)

## Visualisation 1:
S_exponent <- matrix(res[,3], nrow=length(unique(res[,1])), ncol=length(min(scale):(max(scale)/5)))
m_scale <- unique(res[,2])
q <- unique(res[,1])
plot_ly() %>% add_surface(x = ~m_scale, y = ~q,
                         z = ~S_exponent)

## Visualisation 2:
image2D(S_exponent, xlab="q", ylab="scale", axes=F)
axis(1, seq(0,1,0.1), round(quantile(q, seq(0, 1, 0.1)), 2))
axis(2, seq(0,1,0.1), round(quantile(m_scale, seq(0, 1, 0.1)), 2))

## End(Not run)