livpotential_ews {earlywarnings}

Potential Analysis for univariate data

Description

livpotential_ews performs one-dimensional potential estimation derived from a uni-variate timeseries.

Usage

livpotential_ews(
  x,
  std = 1,
  bw = "nrd",
  weights = c(),
  grid.size = NULL,
  detection.threshold = 1,
  bw.adjust = 1,
  density.smoothing = 0,
  detection.limit = 1
)

Arguments

x

Univariate data (vector) for which the potentials shall be estimated

std

Standard deviation of the noise (defaults to 1; this will set scaled potentials)

bw

kernel bandwidth estimation method

weights

optional weights in ksdensity (used by movpotentials).

grid.size

Grid size for potential estimation.

detection.threshold

maximum detection threshold as fraction of density kernel height dnorm(0, sd = bandwidth)/N

bw.adjust

The real bandwidth will be bw.adjust*bw; defaults to 1

density.smoothing

Add a small constant density across the whole observation range to regularize density estimation (and to avoid zero probabilities within the observation range). This parameter adds uniform density across the observation range, scaled by density.smoothing.

detection.limit

minimum accepted density for a maximum; as a multiple of kernel height

return livpotential returns a list with the following elements: xi the grid of points on which the potential is estimated pot The estimated potential: -log(f)*std^2/2, where f is the density. density Density estimate corresponding to the potential. min.inds indices of the grid points at which the density has minimum values; (-potentials; neglecting local optima) max.inds indices the grid points at which the density has maximum values; (-potentials; neglecting local optima) bw bandwidth of kernel used min.points grid point values at which the density has minimum values; (-potentials; neglecting local optima) max.points grid point values at which the density has maximum values; (-potentials; neglecting local optima)

Author(s)

Based on Matlab code from Egbert van Nes modified by Leo Lahti. Implemented in early warnings package by V. Dakos.

References

Livina, VN, F Kwasniok, and TM Lenton, 2010. Potential analysis reveals changing number of climate states during the last 60 kyr . Climate of the Past, 6, 77-82.

Dakos, V., et al (2012).'Methods for Detecting Early Warnings of Critical Transitions in Time Series Illustrated Using Simulated Ecological Data.' PLoS ONE 7(7): e41010. doi:10.1371/journal.pone.0041010

Examples

data(foldbif)
res <- livpotential_ews(foldbif[,1])