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Interleaved eCOCO (odd/even cross-validated evolutionary COCO)

Source: R/ecoco_interleaved.R
ecoco_interleaved.Rd

Interleaved eCOCO evaluates complete sliding windows of the cleaned (finite, sorted, duplicate-averaged) record. Within each window the globally odd observations train a frozen four-group coherent-nine astronomical target that is validated on the globally even observations, and vice versa (Interleaved cvCOCO applied per window). Each fold is linearly regularised at its own median spacing after the split. The consensus correlation is the same-rate minimum of the two directional curves; its global p-value is a plus-one Monte Carlo p against the null maximum over the complete rate grid. Each null realisation is one stationary Gaussian AR(1) process on the complete window order, split and interpolated like the data. Windows that cannot be resolved for the rate grid are returned empty. pCOCO = rho * |log10(p_global)| is the ridge score. Translated from Acycle v3.1 ecocoInterleavedCore.m, interleavedcvcoco.m and cvcoco.m (Mingsong Li). Requires the cocoR helpers (part of this package).

Usage

ecoco_interleaved(
  data = NULL,
  orbit9 = c(405.6912, 130.6979, 123.8532, 98.8517, 94.8856, 40.9897, 23.682, 22.3758,
    18.9519),
  window = NULL,
  sr = NULL,
  step_depth = NULL,
  step = 1,
  pad = NULL,
  red = 0,
  n_sim = 2000,
  method = "Pearson",
  max_frequency = NULL,
  seed = 1,
  window_mode = "physical-depth",
  dt = NULL,
  batch_size = 20,
  genplot = FALSE,
  verbose = FALSE
)

Arguments

data

Record to analyse (matrix or data frame, two columns): depth in metres in column 1 and the proxy in column 2 (at least 16 unique depths). Give the raw, possibly irregular data; do not interpolate beforehand, because the odd and even observations are split before each fold is regularised. Non-finite rows are dropped, rows sorted and duplicated depths averaged. Required (Default=NULL).

orbit9

The nine astronomical target periods in kyr (numeric vector of nine distinct positive values: long eccentricity, four short eccentricity terms, obliquity, three precession terms), e.g. from orbit9_at_age for the age of the record. Default=c(405.6912, 130.6979, 123.8532, 98.8517, 94.8856, 40.9897, 23.6820, 22.3758, 18.9519).

window

Length of the sliding window, in metres (numeric, > 0, at most the record span; windows with fewer than 16 observations are left empty). NULL uses 25% of the record length. Default=NULL.

sr

Sedimentation rates to test, in cm/kyr (numeric vector, > 0, strictly increasing with a constant step). NULL uses the Acycle GUI default: from 2 * dt * 0.065 * 100 up to 100 cm/kyr (reduced so that the longest period fits in the record), in steps of 0.1 cm/kyr or at most 300 steps. Default=NULL.

step_depth

Spacing of the window centres, in metres (numeric, > 0); only used with window_mode="physical-depth". NULL uses dt, or dt * ceiling(n / 300) for more than 300 samples. Default=NULL.

step

Step between successive windows, in samples (integer, >= 1); only used with window_mode="legacy-count". Default=1.

pad

Length (number of points) to which the periodogram of each fold is zero-padded; each fold uses max(pad, fold length) (integer, > 0). NULL uses the Acycle default: 5000 for up to 2500 samples, 10000 for up to 5000 samples, and floor(n / 5000) * 5000 + 5000 above that. Default=NULL.

red

Background (red-noise) removal applied to every spectrum (integer): 0 none, 1 classical AR(1) background, 2 robust AR(1) background, 3 smoothed-window-average (SWA) background. Default=0.

n_sim

Number of AR(1) Monte Carlo simulations per window used for the global and local p-values (integer, >= 0). Default=2000.

method

Correlation coefficient between the data and target spectra (character): "Pearson" or "Spearman". Default="Pearson".

max_frequency

Highest frequency of the target spectrum that enters the correlation, in cycles/kyr (numeric, at least max(1/orbit9)); NULL uses 1.2 * max(1/orbit9). Default=NULL.

seed

Parent seed of the random number generator (integer). Each window uses a seed derived from it and from the window position (Acycle deriveWindowSeed), so results are reproducible and independent of the other windows; NULL leaves the current random state unchanged. Default=1.

window_mode

How the windows are defined (character): "physical-depth" (windows of fixed length in metres centred every step_depth) or "legacy-count" (windows of a fixed, even number of points, window / dt + 1 rounded, at least 16, moved by step samples). Default="physical-depth".

dt

Nominal sampling interval, in metres (numeric, > 0), used for the number of points per window in "legacy-count" mode and for the defaults of step_depth and sr. NULL uses the median spacing of the cleaned data. Default=NULL.

batch_size

Number of Monte Carlo simulations processed together (integer, >= 1); larger batches are faster but use more memory. Default=20.

genplot

Plot the result with plot_ecoco_cv (logical, TRUE or FALSE). Default=FALSE.

verbose

Print messages and a progress bar over the windows (logical, TRUE or FALSE). Default=FALSE.

Value

A list (class "ecoco_cv") with method, sr, depth, rate-by-window matrices rho, p_global, p_local, norbit, pcoco, score, lists forward (odd -> even), backward (even -> odd), consensus and strict (consensus curve with the larger directional p), windows (data frame: bounds, point counts, parity phase, derived seed, success, window-level p-values, fold spacings, all-nine rate ranges, AR(1) rho), best and track.

References

Li, M., Kump, L.R., Hinnov, L.A., Mann, M.E., 2018. Tracking variable sedimentation rates and astronomical forcing in Phanerozoic paleoclimate proxy series with evolutionary correlation coefficients and hypothesis testing. Earth and Planetary Science Letters 501, 165-179. doi:10.1016/j.epsl.2018.08.041

Author

Michiel Arts (R translation); original MATLAB code: Mingsong Li

Examples

# \donttest{
set.seed(2)
dt <- 0.05
depth <- seq(0, 30, by = dt)
tt <- depth * 100 / 5
x <- sin(2 * pi * tt / 405.7) + 0.8 * sin(2 * pi * tt / 98.9) +
  0.5 * sin(2 * pi * tt / 40.99) + 0.4 * sin(2 * pi * tt / 23.68) +
  0.3 * rnorm(length(tt))
res <- ecoco_interleaved(cbind(depth, x), window = 15,
                         sr = seq(3, 8, 0.5), step_depth = 2, pad = 400,
                         n_sim = 20)
res$track[, c("depth", "sr")]
#>   depth  sr
#> 1   7.5 5.5
#> 2   9.5 5.5
#> 3  11.5 5.5
#> 4  13.5 3.5
#> 5  15.5 5.5
#> 6  17.5 5.5
#> 7  19.5 3.5
#> 8  21.5 3.5
# }