Detrended fluctuation analysis (DFA)

Estimates the DFA scaling exponent \(\alpha\). White noise gives \(\alpha \approx 0.5\); pink (1/f) noise \(\alpha \approx 1.0\); Brownian motion \(\alpha \approx 1.5\).

Usage

dfa(x, scales = NULL)

Arguments

x

Numeric vector (length \(\geq\) 16).

scales

Integer vector of window sizes (auto-generated if NULL).

Value

List with value (alpha), name, and extra (scales, fluctuation).

Details

Reference: 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(1):82–87.

Examples

# \donttest{
set.seed(1)
x <- cumsum(rnorm(2048))
res <- dfa(x)
res$value
#> [1] 1.424271
# }