Estimates the fractal dimension of a time series using Higuchi's (1988)
curve-length algorithm. A clean-room C++ reimplementation, validated
against a MATLAB reference implementation on synthetic test data — see
inst/COPYRIGHTS.
Usage
higuchi_fd(x, k_max = 10L)
Arguments
- x
Numeric vector. The time series to analyse.
- k_max
Integer (>= 2). Maximum sub-series interval k. Choose
based on where the log-log curve plateaus for your signal (see Doyle
et al. for guidance in postural-sway / physiological contexts).
Value
A list with:
- k
The k values evaluated, 1:k_max.
- L
Average curve length at each k.
- hfd
The Higuchi Fractal Dimension: negative slope of log(L)
on log(1/k).
References
Higuchi T. Approach to an irregular time series on the basis of the
fractal theory. Physica D 1988;31(2):277-283.
Examples
set.seed(1)
higuchi_fd(rnorm(1000), k_max = 10)
#> $k
#> [1] 1 2 3 4 5 6 7 8 9 10
#>
#> $L
#> [1] 1204.12194 297.33968 131.25692 73.58719 46.49776 34.08144
#> [7] 23.10696 18.47379 14.18394 11.63339
#>
#> $hfd
#> [1] 2.015343
#>