Higuchi fractal dimension

Estimates the Higuchi (1988) fractal dimension of a 1-D time series via length scaling across k time-lags. Values typically fall in [1, 2]; higher values indicate greater signal complexity.

Usage

hfd(x, kmax = 10L)

Arguments

x

Numeric vector (length \(\geq\) 4).

kmax

Maximum k (default 10).

Value

List with value (D), name, and extra (kmax, n, L_k).

Details

Reference: Higuchi, T. (1988) "Approach to an irregular time series on the basis of the fractal theory", Physica D 31(2):277–283.

Examples

# \donttest{
set.seed(1)
x <- cumsum(rnorm(1000))
hfd(x, kmax = 10)$value
#> [1] 1.559051
# }