DFA {DFA}

Detrended Fluctuation Analysis (DFA)

Description

Applies the Detrended Fluctuation Analysis (DFA) to nonstationary time series.

Usage

DFA(file,scale = 2^(1/8),box_size = 4,m=1)

Arguments

file

Univariate time series (must be a vector or data frame)

scale

Specifies the ratio between successive box sizes (by default scale = 2^(1/8))

box_size

Vector of box sizes (must be used in conjunction with scale = "F")

m

An integer of the polynomial order for the detrending (by default m=1).

Details

The DFA fluctuation can be computed in a geometric scale or for different choices of boxes sizes.

Value

boxe

Size n of the overlapping boxes.

DFA

Detrended Fluctuation function.

Note

The time series file and file2 must have the same sample size.

Author(s)

Victor Barreto Mesquita

References

C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger Phys. Rev. E, 49 (1994), p. 1685

H.E. Stanley, L.A.N. Amaral, A.L. Goldberger, S. Havlin, P.Ch. Ivanov, C.-K. Peng Physica A, 270 (1999), p. 309

P.C. Ivanov, A. Bunde, L.A.N. Amaral, S. Havlin, J. Fritsch-Yelle, R.M. Baevsky, H.E. Stanley, A.L. Goldberger Europhys. Lett., 48 (1999), p. 594

P. Talkner, R.O. Weber Phys. Rev. E, 62 (2000), p. 150

M. Ausloos, K. Ivanova Physica A, 286 (2000), p. 353

H.E. Hurst, R.P. Black, Y.M. Simaika Long-Term Storage, An Experimental Study, Constable, London (1965)

Examples

#The following examples using the database of financial time series
#collected during the United States bear market of 2007-2009.

library(DFA)
data("NYA2008")
file = NYA2008

DFA(file,scale = 2^(1/8),box_size = c(4,8,16),m=1)


# Example with different polynomial fit order.

library(DFA)
data("LSE.L2008")
file = LSE.L2008

DFA(file,scale = 2^(1/8),box_size = c(4,8,16),m=2)


# Example using different choice of overlapping boxes sizes.

library(DFA)
data("NYA2008")
file = NYA2008

DFA(file,scale = "F",box_size = c(4,8,16),m=1)