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Evolutionary lag-1 autocorrelation coefficient (rho1)

Source: R/rho1_evolutive.R
rho1_evolutive.Rd

The rho1_evolutive function calculates the lag-1 autocorrelation coefficient of an AR(1) model in moving windows, as used in the sedimentary noise model of Li et al. (2018a,b). With n_sim = 0 a single deterministic run is made (acycleEvolutionaryRho1.m): the series is linearly interpolated on a grid anchored at the first coordinate with interval sample_min, windows of round(window_min/sample_min) points are linearly detrended and rho1 = sum(z[t] z[t-1]) / sum(z[t-1]^2) of the demeaned residuals z is reported at the midpoint of each window. With n_sim > 0 the Acycle Monte Carlo is run (AC.m menu "Lag-1 autocorrelation coefficient (rho1)"): for every simulation a sampling interval and a window are drawn uniformly from [sample_min, sample_max] and [window_min, window_max], the data are linearly interpolated (interpolate.m), evolutionary rho1 is computed with erhoAR1.m (window of round(window/dt) points, linear detrending, rhoAR1ML.m), window centers are optionally shifted by a random offset uniform in [-window/2, window/2], and the curves are linearly interpolated on a regular grid and summarized by the percentiles 2.5, 5, 10, 15.865, 25, 50, 75, 84.135, 90, 95 and 97.5. Translated from Acycle v3.1 acycleEvolutionaryRho1.m, acycleInterpolateSeries.m, erhoAR1.m, rhoAR1ML.m, interpolate.m and AC.m (menu_rho_Callback) (Mingsong Li; rhoAR1 by Dorothee Husson).

Usage

rho1_evolutive(
  data = NULL,
  window_min = NULL,
  window_max = NULL,
  sample_min = NULL,
  sample_max = NULL,
  n_sim = 1000,
  n_out = NULL,
  shift_grid = TRUE,
  seed = NULL,
  verbose = FALSE,
  genplot = FALSE
)

Arguments

data

Proxy record (required): matrix or data frame with depth/time in column 1 and the proxy value in column 2 (further columns are ignored). Rows with non-finite values are removed and the rows are sorted by depth/time; the depth/time values must be unique. Default=NULL.

window_min

Window length in depth/time units (numeric, > 0): the window of the single run (n_sim = 0) or the shortest window drawn in the Monte Carlo run. NULL: min(400, 0.3 * L) where L is the length of the record (in the Monte Carlo run 400 if 0.3 * L > 400, otherwise 0.3 * L). In the single run the window must span at least three interpolated points. Default=NULL.

window_max

Longest window drawn in the Monte Carlo run, in depth/time units (numeric, >= window_min); not used when n_sim = 0. NULL: 500 if 0.3 * L > 400, otherwise 0.4 * L. Default=NULL.

sample_min

Interpolation interval in depth/time units (numeric, > 0): the interval of the single run or the smallest interval drawn in the Monte Carlo run. NULL uses the 95th percentile of the sampling intervals of data. Default=NULL.

sample_max

Largest interpolation interval drawn in the Monte Carlo run, in depth/time units (numeric, >= sample_min); not used when n_sim = 0. NULL uses twice the 95th percentile of the sampling intervals. Default=NULL.

n_sim

Number of Monte Carlo simulations (integer, 0 or >= 50, as in Acycle). 0 gives a single deterministic run with window_min and sample_min. Default=1000.

n_out

Number of points of the regular depth/time grid on which the Monte Carlo curves are interpolated and summarised (integer, > 1). NULL: min(1000, number of data points). Default=NULL.

shift_grid

Shift the window centres of every simulation by a random offset, uniform between minus and plus half the window length (logical; Acycle "shift grids" > 1). Only used in the Monte Carlo run. Default=TRUE.

seed

Seed of the random number generator (integer), so that the Monte Carlo results can be reproduced; NULL leaves the current random state unchanged. Default=NULL.

verbose

Show a progress bar of the Monte Carlo simulations (logical, TRUE or FALSE). Default=FALSE.

genplot

Plot the result (logical): the rho1 curve of the single run, or the percentile bands with the median of the Monte Carlo run. Default=FALSE.

Value

For n_sim = 0 a list with rho1 (matrix [window center, rho1]), window_points, sample_interval and window. For the Monte Carlo a list with percentile (matrix [x, 11 percentiles] on the grid points where they are defined), median (matrix [x, median]), percentiles, grid, rho1 (n_out x n_sim matrix of all realisations) and draws (sampling intervals, windows, shifts).

References

Li, M., Hinnov, L.A., Huang, C., Ogg, J.G., 2018a. Sedimentary noise and sea levels linked to land-ocean water exchange and obliquity forcing. Nature Communications 9, 1004. doi:10.1038/s41467-018-03454-y

Li, M., Huang, C., Hinnov, L., Chen, W., Ogg, J., Tian, W., 2018b. Astrochronology of the Anisian stage (Middle Triassic) at the Guandao reference section, South China. Earth and Planetary Science Letters 482, 591-606. doi:10.1016/j.epsl.2017.11.042

Mudelsee, M., 2002. TAUEST: a computer program for estimating persistence in unevenly spaced weather/climate time series. Computers & Geosciences 28, 69-72.

Author

Michiel Arts (R translation); original MATLAB code: Mingsong Li (Acycle), rhoAR1 by Dorothee Husson.

Examples

# \donttest{
set.seed(3)
t <- cumsum(runif(800, 0.5, 1.5))
x <- as.numeric(arima.sim(list(ar = 0.8), n = 800))
single <- rho1_evolutive(data = cbind(t, x), n_sim = 0)
mc <- rho1_evolutive(data = cbind(t, x), n_sim = 50, seed = 1,
  genplot = TRUE)

# }