multivariate-DFA in R

Multivariate DFA (detrended fluctuation analysis) in R, adapted from: https://github.com/spiralizing/InfoSeries.jl/blob/master/src/func_series.jl

Repository files

• Multi_DFA.R: core dfa_function(x, pol, sec) implementation.
• get_scale_function.R: helper that builds log-spaced window scales.
• plot_dfa.R: helper function to plot DFA output (log(s) vs log(F(s))).
• run_dfa.R: complete runnable example using the sample CSV.
• helper_dfa_params.R: helper to compare (pol, n_scales) combinations and rank them.
• colored_noise_utils.R: utilities to generate white/pink/brown/blue noise signals.
• run_colored_noise_demo.R: demo that generates colored-noise test data and estimates alpha for each noise type.
• todasvocesRESC.csv: sample multivariate time-series input.

Input format

Your input must be a data.frame where:

1. Column 1 is time/index.
2. Columns 2..N are signals (one signal per column).

Example header from sample data:

time,V1,V2,...

Quick start

source("get_scale_function.R")
source("Multi_DFA.R")
source("plot_dfa.R")

x <- read.csv("todasvocesRESC.csv")
pol <- 1
sec <- get_scale(x[[2]], 20)

result <- dfa_function(x, pol, sec)
dplot <- result$dplot
alpha <- result$alpha

library(ggplot2)
p <- plot_dfa(dplot, "Multivariate DFA")
print(p)

Or just run:

Rscript run_dfa.R

This will create:

• alphadfa.txt (estimated alpha)
• dfa_plot.png (scatter plot)

Notes

• sec should contain increasing window sizes; get_scale() handles this.
• pol is polynomial detrending order (common first try: pol = 1).

Optional helper: choose pol and n_scales

source("get_scale_function.R")
source("Multi_DFA.R")
source("helper_dfa_params.R")

x <- read.csv("todasvocesRESC.csv")
out <- choose_dfa_params(
  x,
  pol_values = c(1, 2, 3),
  n_scales_values = c(12, 20, 30),
  signal_col = 2
)

out$results  # all combinations sorted by R^2
out$best     # top-ranked row

If one combination fails (for example, a singular fit inside DFA), the helper now marks that row with status = "error" and stores the message in error instead of stopping the full search.

Colored-noise validation demo

You can generate test signals (white, pink, brown, blue noise) and run DFA on each:

Rscript run_colored_noise_demo.R

This script:

• creates colored_noise_test.csv with columns time, white, pink, brown, blue
• runs DFA on each signal with shared pol = 1 and shared scales (n_scales = 20)
• writes colored_noise_alpha_results.csv with expected vs estimated alpha values
• saves one diagnostic figure per color:
  • colored_noise_white_diagnostic.png
  • colored_noise_pink_diagnostic.png
  • colored_noise_brown_diagnostic.png
  • colored_noise_blue_diagnostic.png (left panel: log-log power spectrum, right panel: DFA log-log plot)
  • spectrum fit now uses the central frequency band (5% to 95%) for a more stable beta_est

Expected alpha reference (approximate):

• white noise: ~0.5
• pink noise: ~1.0
• brown noise: ~1.5
• blue noise: ~0.0

Note: blue noise can show larger alpha deviations in finite-length samples because anti-correlated signals are more sensitive to scale range and detrending choices. Also, colored-noise generation uses random complex Fourier coefficients (not fixed magnitudes), so pink and brown spectra should have distinct slopes but realistic variability between runs.