MFXDFA: Multifractal detrended cross-correlation analysis

In mlaib/MFDFA: MultiFractal Detrended Fluctuation Analysis

Description

Applies the MultiFractal Detrended Fluctuation cross-correlation Analysis (MFXDFA) on two time series.

Usage

MFXDFA(tsx1, tsx2, scale, m=1, q)

Arguments

tsx1	Univariate time series (must be a vector or a ts object).
tsx2	Univariate time series (must be a vector or a ts object).
scale	Vector of scales.
m	Polynomial order for the detrending (by default m=1).
q	q-order of the moment. There is no default value for this parameter, please add values.

Value

A list of the following elements:

• Hq Hurst exponent.

• h Holder exponent.

• Dh Multifractal spectrum.

• Fq Fluctuation function in log.

Note

The original code of this function is in Matlab, you can find it on the following website Mathworks.

References

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

Espen A. F. Ihlen, Introduction to multifractal detrended fluctuation analysis in matlab, Frontiers in Physiology: Fractal Physiology, 3 (141),(2012) 1-18.

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.

Kantelhardt J.W. (2012) Fractal and Multifractal Time Series. In: Meyers R. (eds) Mathematics of Complexity and Dynamical Systems. Springer, New York, NY.

Examples

library(MFDFA)
a<-0.6
N<-1024

tsx1<-MFsim(N,a)
b<-0.8
N<-1024

tsx2<-MFsim(N,b)
scale=10:100
q<--10:10
m<-1

## Not run: 
b<-MFXDFA(tsx1, tsx2, scale, m=1, q)

## Supplementary functions: #####
reset <- function(){
par(mfrow=c(1, 1), oma=rep(0, 4), mar=rep(0, 4), new=TRUE)
plot(0:1, 0:1, type="n", xlab="", ylab="", axes=FALSE)}

poly_fit<-function(x,y,n){
  formule<-lm(as.formula(paste('y~',paste('I(x^',1:n,')', sep='',collapse='+'))))
  res1<-coef(formule)
  poly.res<-res1[length(res1):1]
  allres<-list(polyfit=poly.res, model1=formule)
  return(allres)}

## Plot results: #####
dev.new()
layout(matrix(c(1,2,3,4), 2, 2, byrow = TRUE),heights=c(4, 4))
## b : mfdfa output
par(mai=rep(0.8, 4))

## 1st plot: Fluctuations function
p1<-which(q==2)
plot(log(scale),b$Fq[,p1],  pch=16, col=1, axes = FALSE, xlab = "s",
     ylab=expression('log'*'(F'[2]*')'), cex=1, cex.lab=1.6, cex.axis=1.6,
     main= "Fluctuation function F for q=2",
     ylim=c(min(b$Fq[,c(p1)]),max(b$Fq[,c(p1)])))
lines(log(scale),b$line[,p1], type="l", col=1, lwd=2)
grid(col="midnightblue")
axis(2)
lbl<-scale[c(1,floor(length(scale)/8),floor(length(scale)/4),
             floor(length(scale)/2),length(scale))]
att<-log(lbl)
axis(1, at=att, labels=lbl)

## 2nd plot: q-order Hurst exponent
plot(q, b$Hq, col=1, axes= FALSE, ylab=expression('h'[q]), pch=16, cex.lab=1.8,
     cex.axis=1.8, main="Hurst exponent", ylim=c(min(b$Hq),max(b$Hq)))
grid(col="midnightblue")
axis(1, cex=4)
axis(2, cex=4)

## 3rd plot: Spectrum
plot(b$h, b$Dh, col=1, axes=FALSE, pch=16, main="Multifractal spectrum",
     ylab=bquote("f ("~alpha~")"),cex.lab=1.8, cex.axis=1.8,
     xlab=bquote(~alpha))
grid(col="midnightblue")
axis(1, cex=4)
axis(2, cex=4)

x1=b$h
y1=b$Dh
rr<-poly_fit(x1,y1,4)
mm1<-rr$model1
mm<-rr$polyfit
x2<-seq(min(x1),max(x1)+1,0.01)
curv<-mm[1]*x2^4+mm[2]*x2^3+mm[3]*x2^2+mm[4]*x2+mm[5]
lines(x2,curv, col="red", lwd=2)

## End(Not run)

mlaib/MFDFA documentation built on June 14, 2019, 2:14 p.m.