hurst: Hurst coefficient

Description

The function estimates the Hurst coefficient of a process

Usage

hurst(x, y = NULL, z = NULL, data,
      gridtriple = FALSE, sort = TRUE,
      block.sequ = unique(round(exp(seq(log(3000), log(dim[1]),
                          len=min(100, dim[1]))))),
      fft.m = c(1, min(1000, (fft.len - 1) / 10)),
      fft.max.length = Inf, method=c("dfa", "fft", "var"),
      mode=c("plot", "interactive"), pch=16, cex=0.2, cex.main=0.85,
      PrintLevel=RFparameters()$Print,height=3.5,...)

Arguments

matrix of coordinates, or vector of x coordinates

vector of y coordinates

vector of z coordinates

data

the data

gridtriple

logical. Only relevant if grid==TRUE. If gridtriple==TRUE then x, y, and z are of the form c(start,end,step); if gridtriple==FALSE then x

sort

logical. If TRUE then the coordinates are permuted such that the largest grid length is in x-direction; this is of interest for algorithms that slice higher dimensional fields into one-dimensional sections.

block.sequ

ascending sequences of block lengths for which the detrended fluctuation analysis and the variance method is performed.

fft.m

vector of 2 integers; lower and upper endpoint of indices for the frequency which are used in the calculation of the regression line for the periodogram near the origin.

fft.max.length

if the number of points in x-direction is larger than fft.max.length then the segments of length fft.max.length are considered, shifted by fft.max.length/2 (WOSA-estimator).

method

list of implemented methods to calculate the Hurst parameter; see Details

mode

character. A vector with components 'nographics', 'plot', or 'interactive': [object Object],[object Object],[object Object] Usually only one mode is given. Two modes may make sense in the combination c("plot", "interactive") in which case

pch

vector or scalar; sign by which data are plotted.

cex

vector or scalar; size of pch.

cex.main

font size for title in regression plot, see regression; only used if mode includes 'plot' or 'interactive'

PrintLevel

integer. If PrintLevel is 0 or 1 nothing is printed. If PrintLevel==2 warnings and the regression results are given. If PrintLevel>2 tracing information is given.

height

height of the graphics window

...

graphical parameters

Value

The function returns a list with elements dfa, varmeth, fft corresponding to the three methods given in the Details. Each of the elements is itself a list that contains the following elements.
xthe x-coordinates used for the regression fit
ythe y-coordinates used for the regression fit
regrthe coefficients of the lm
smsmoothed curve through the (x,y) points
x.uNULL or the restricted x-coordinates given by the user in the interactive plot
y.uNULL or y-coordinates according to x.u
regr.uNULL or the coefficients of lm for x.u and y.u
Hthe Hurst coefficient
H.uNULL or the Hurst coefficient corresponding to the user's regression line

Details

The function is still in development. Several functionalities do not exist - see the code itself for the current stage.

The function calculates the Hurst coefficient by various methods:

detrended fluctuation analysis (dfa)
aggregated variation (var)
periodogram or WOSA estimator (fft)

References

detrended fluctuation analysis

Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E. and Goldberger, A.L. (1994) Mosaic organization of DNA nucleotidesPhys. Rev. E49, 1685-1689

aggregated variation

Taqqu, M.S. and Teverovsky, V. (1998) On estimating the intensity of long range dependence in finite and infinite variance time series. In: Adler, R.J., Feldman, R.E., and Taqqu, M.S.A Practical Guide to Heavy Tails, Statistical Techniques an Applications.Boston: Birkhaeuser
Taqqu, M.S. and Teverovsky, V. and Willinger, W. (1995) Estimators for long-range dependence: an empirical study.Fractals3, 785-798

periodogram