DFA {mvDFA}

Analyze univariate time series and estimate long memory using Detrended Fluctuations Analysis (DFA; Peng et al., 1995)

Description

Analyze univariate time series and estimate long memory using Detrended Fluctuations Analysis (DFA; Peng et al., 1995)

Usage

DFA(X, steps = 50, brownian = FALSE, degree = 1, verbose = TRUE, cores = 1)

Arguments

X

Univariate time series.

steps

Maximum number of window sizes. These are spread logarithmically. If time series is short and steps is large, fewer window sizes are drawn. Default to 50.

brownian

Indicator whether time series is assumed to be brownian (i.e. variance increases proportional to time)

degree

The maximum order of the detrending polynomial in the segments. This influences the smallest window size minS such that minS = degree + 2.

verbose

Indicator whether additional info should be printed. Default to TRUE.

cores

Number of cores used in computation. Default to 1.

Value

Returns list of Root Mean Squares per window size RMS_s, the window sizes S and the estimated long memory coefficient L - the Hurst Exponent.

References

Peng, C. K., Havlin, S., Stanley, H. E., & Goldberger, A. L. (1995). Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time-series. Chaos, 5, 82–87. <doi:10.1063/1.166141>

Examples

X <- rnorm(500) # generate Gaussian white noise (i.i.d. standard normal variables)
DFA(X = X, steps = 5) # steps = 5 is only for demonstration,
                        # use many steps instead, e.g. steps = 50!