Description Usage Arguments Details Value References See Also Examples
The function estimates the Hurst coefficient of a process
1 2 3 4 5 6 7 8 9 10  RFhurst(x, y = NULL, z = NULL, data, sort = TRUE,
block.sequ = unique(round(exp(seq(log(min(3000, dimen[1]/5)),
log(dimen[1]),
len = min(100, dimen[1]))))),
fft.m = c(1, min(1000, (fft.len  1)/10)),
fft.max.length = Inf, method = c("dfa", "fft", "var"),
mode = if (interactive ()) c("plot", "interactive") else "nographics",
pch = 16, cex = 0.2, cex.main = 0.85,
printlevel = RFoptions()$basic$printlevel, height = 3.5,
...)

x 
\argX 
y,z 
\argYz 
data 
the data 
sort 
logical. If 
block.sequ 
ascending sequences of block lengths for which the detrended fluctuation analysis and the variance method are 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 
method 
list of implemented methods to calculate the Hurst parameter; see Details 
mode 
character. A vector with components
Usually only one mode is given. Two modes may make sense in the combination c("plot", "interactive") in which case all the results are plotted first, and then the interactive mode is called. In the interactive mode, the regression domain is chosen by two mouse clicks with the left mouse; a right mouse click leaves the plot. 
pch 
vector or scalar; sign by which data are plotted. 
cex 
vector or scalar; size of 
cex.main 
font size for title in regression plot;
only used if mode includes 
printlevel 
integer. If 
height 
height of the graphics window 
... 
graphical arguments 
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)
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.
x 
the xcoordinates used for the regression fit 
y 
the ycoordinates used for the regression fit 
regr 
the coefficients of the 
sm 
smoothed curve through the (x,y) points 
x.u 

y.u 

regr.u 

H 
the Hurst coefficient 
H.u 

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 nucleotides Phys. Rev. E 49, 16851689
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 longrange dependence: an empirical study. Fractals 3, 785798
periodogram
Percival, D.B. and Walden, A.T. (1993) Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge: Cambridge University Press.
Welch, P.D. (1967) The use of Fast Fourier Transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms IEEE Trans. Audio Electroacoustics 15, 7073.
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