## log-amplitude Detrended Fluctuation Analysis (DeltaDFA)

### Description

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

### Usage

DeltaDFA(file,file2,scale = 2^(1/8),box_size = 4,m=1)


### Arguments

 file Univariate time series (must be a vector or data frame) file2 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 log-amplitude fluctuation can be computed in a geometric scale or for different choices of boxes sizes.

### Value

 boxe Size n of the overlapping boxes. DeltaDFA log-amplitude Detrended Fluctuation function defined as the difference between the DFA decimal logarithmic of the first time series (file) and the DFA decimal logarithmic of the second time series (file2)

### Note

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

### Author(s)

Victor Barreto Mesquita

### References

G. F. Zebende, F. M. Oliveira Filho, J. A. L. Cruz, Auto-correlationin the motor/imaginary human eeg signals: A vision about the fdfafluctuations, PloS one 12 (9) (2017).

F. Oliveira Filho, J. L. Cruz, G. Zebende, Analysis of the eeg bio-signalsduring the reading task by dfa method, Physica A: Statistical Mechanicsand its Applications 525 (2019) 664-671.

S. R. Hirekhan, R. R. Manthalkar, The detrended fluctuation and cross-correlation analysis of eeg signals, International Journal of IntelligentSystems Design and Computing 2 (2) (2018) .

### 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")
data("IXIC2008")
file = NYA2008
file2= IXIC2008

# Example with different polynomial fit order.

library(DFA)
data("NYA2008")
data("LSE.L2008")
file = NYA2008
file2= LSE.L2008

# Example using differente choice of overlapping boxes sizes.

library(DFA)
data("NYA2008")
data("IXIC2008")
file = NYA2008
file2= IXIC2008