GGIR (version 3.3-8)

SSP: Estimated self-similarity parameter

Description

This function estimates the overall self-similarity parameter (SSP), also known as the scaling exponent or alpha, as well as the piecewise short-term (alpha_1) and long-term (alpha_2) scaling exponents.

Usage

SSP(data, scale = 2^(1/8), box_size = 4, m = 1, epochSize)

Value

A list containing three real numbers (all of them between 0 and 2):

alpha_overall

The overall estimated scaling exponent across all box sizes.

alpha_1

The short-term scaling exponent, calculated for time scales smaller than or equal to 90 minutes.

alpha_2

The long-term scaling exponent, calculated for time scales between 120 and 600 minutes.

Arguments

data

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)

epochSize

The epoch size of the data in seconds. Used to convert box sizes to minutes to apply time boundaries for alpha_1 and alpha_2.

Author

Ian Meneghel Danilevicz <[e-mail]> Victor Barreto Mesquita <[e-mail]> Jairo H Migueles <[e-mail]>

Details

The DFA fluctuation can be computed in a geometric scale or for different choices of boxes sizes. In human motor activity, the scaling behavior exhibits a crossover point around 1.5 to 2 hours. Therefore, alpha_1 captures the short-term temporal correlations regulated by multiple physiological controls, while alpha_2 captures long-term fluctuations that are heavily reliant on the central circadian pacemaker.

References

C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger Phys. Rev. E, 49 (1994), p. 1685 Mesquita, Victor & Filho, Florencio & Rodrigues, Paulo. (2020). Detection of crossover points in detrended fluctuation analysis: An application to EEG signals of patients with epilepsy. Bioinformatics. 10.1093/bioinformatics/btaa955.

Examples

  # Estimate self-similarity of a very known time series available on R base: the sunspot.year.
  # Then the spend time with each method is compared.
  if (FALSE) {
    ssp_results = SSP(sunspot.year)
    ssp_results$alpha_overall
    ssp_results$alpha_1
    ssp_results$alpha_2
  }