Multi-fractal Detrended Fluctuation Analysis

fd_mfdfa(
  y,
  fs = NULL,
  removeTrend = c("no", "poly", "adaptive", "bridge")[2],
  polyOrder = 1,
  standardise = c("none", "mean.sd", "median.mad")[1],
  adjustSumOrder = FALSE,
  removeTrendSegment = c("no", "poly", "adaptive", "bridge")[2],
  polyOrderSegment = 1,
  scaleMin = 16,
  scaleMax = stats::nextn(floor(NROW(y)/4), factors = 2),
  scaleResolution = round(log2(scaleMax - scaleMin)),
  dataMin = NA,
  scaleS = NA,
  overlap = NA,
  qq = seq(-5, 5, length.out = 101),
  doPlot = FALSE,
  returnPlot = FALSE,
  returnInfo = FALSE,
  silent = FALSE
)

Arguments

y: A numeric vector or time series object.
fs: Sample rate
removeTrend: Method to use for global detrending (default = "poly")
polyOrder: Order of global polynomial trend to remove if removeTrend = "poly". If removeTrend = "adaptive" polynomials 1 to polyOrder will be evaluated and the best fitting curve (R squared) will be removed (default = 1)
standardise: Standardise the series using ts_standardise() with adjustN = FALSE (default = "mean.sd")
adjustSumOrder: Adjust the time series (summation or difference), based on the global scaling exponent, see e.g. Ihlen (2012) (default = FALSE)
removeTrendSegment: Method to use for detrending in the bins (default = "poly")
polyOrderSegment: The DFA order, the order of polynomial trend to remove from the bin if removeTrendSegment = "poly". If removeTrendSegment = "adaptive" polynomials 1 to polyOrder will be evaluated and the best fitting polynomial (R squared) will be removed (default = 1)
scaleMin: Minimum scale (in data points) to use for log-log regression (default = 4)
scaleMax: Maximum scale (in data points) to use for log-log regression. This value will be ignored if dataMin is not NA, in which case bins of size < dataMin will be removed (default = stats::nextn(floor(NROW(y)/4), factors = 2))
scaleResolution: The scales at which detrended fluctuation will be evaluated are calculated as: seq(scaleMin, scaleMax, length.out = scaleResolution) (default = round(log2(scaleMax-scaleMin))). #' @param dataMin Minimum number of data points in a bin required for inclusion in calculation of the scaling relation. For example if length(y) = 1024 and dataMin = 4, the maximum scale used to calculate the slope will be 1024 / 4 = 256. This value will take precedence over the scaleMax (default = NA)
scaleS: If not NA, it should be a numeric vector listing the scales on which to evaluate the detrended fluctuations. Arguments scaleMax, scaleMin, scaleResolution and dataMin will be ignored (default = NA)
overlap: A number in [0 ... 1] representing the amount of 'bin overlap' when calculating the fluctuation. This reduces impact of arbitrary time series begin and end points. If length(y) = 1024 and overlap is .5, a scale of 4 will be considered a sliding window of size 4 with step-size floor(.5 * 4) = 2, so for scale 128 step-size will be 64 (default = NA)
qq: A vector containing a range of values for the order of fluctuation q (default = seq(-5, 5,length.out=101))
doPlot: Output the log-log scale versus fluctuation plot with linear fit by calling function plotFD_loglog() (default = TRUE)
returnPlot: Return ggplot2 object (default = FALSE)
returnInfo: Return all the data used in SDA (default = FALSE)
silent: Silent-ish mode (default = FALSE)

Value

A dataframe with values of q,H(q), t(q), h(q), `D(q)“

Examples


set.seed(33)

# White noise
fd_mfdfa(rnorm(4096), doPlot = TRUE)
#> 
#> 
#> (mf)dfa:	Sample rate was set to 1.
#> 
#> `geom_smooth()` using formula = 'y ~ x'

#> 
#> ~~~o~~o~~casnet~~o~~o~~~
#> 
#>  Multifractal Detrended FLuctuation Analysis 
#> 
#>   Spec_AUC Spec_Width Spec_CVplus Spec_CVmin Spec_CVtot Spec_CVasymm
#> 1   0.0894     0.0947      0.0455     0.0466     0.0459      -0.0114
#> 
#> 
#> ~~~o~~o~~casnet~~o~~o~~~

# Pink noise
fd_mfdfa(noise_powerlaw(N=4096), doPlot = TRUE)
#> 
#> 
#> (mf)dfa:	Sample rate was set to 1.
#> 
#> `geom_smooth()` using formula = 'y ~ x'

#> 
#> ~~~o~~o~~casnet~~o~~o~~~
#> 
#>  Multifractal Detrended FLuctuation Analysis 
#> 
#>   Spec_AUC Spec_Width Spec_CVplus Spec_CVmin Spec_CVtot Spec_CVasymm
#> 1    0.199      0.217      0.0709      0.104     0.0892       -0.189
#> 
#> 
#> ~~~o~~o~~casnet~~o~~o~~~

# 'multi' fractal
N <- 2048
y <- rowSums(data.frame(elascer(noise_powerlaw(N=N, alpha = -2)), elascer(noise_powerlaw(N=N, alpha = -.5))*c(rep(.2,512),rep(.5,512),rep(.7,512),rep(1,512))))
fd_mfdfa(y=y, doPlot = TRUE)
#> 
#> 
#> (mf)dfa:	Sample rate was set to 1.
#> 
#> `geom_smooth()` using formula = 'y ~ x'

#> 
#> ~~~o~~o~~casnet~~o~~o~~~
#> 
#>  Multifractal Detrended FLuctuation Analysis 
#> 
#>   Spec_AUC Spec_Width Spec_CVplus Spec_CVmin Spec_CVtot Spec_CVasymm
#> 1    0.212      0.246      0.0732      0.176       0.14       -0.412
#> 
#> 
#> ~~~o~~o~~casnet~~o~~o~~~

Multi-fractal Detrended Fluctuation Analysis

Arguments

Value

See also

Examples