earlywarnings (version 1.0.59)

ddjnonparam_ews: Description: Drift Diffusion Jump Nonparametrics Early Warning Signals

Description

ddjnonparam_ews is used to compute nonparametrically conditional variance, drift, diffusion and jump intensity in a timeseries. It also interpolates to obtain the evolution of the nonparametric statistics in time.

Usage

ddjnonparam_ews(timeseries, bandwidth = 0.6, na = 500, logtransform = TRUE, interpolate = FALSE)

Arguments

timeseries

a numeric vector of the observed univariate timeseries values or a numeric matrix where the first column represents the time index and the second the observed timeseries values. Use vectors/matrices with headings.

bandwidth

is the bandwidht of the kernel regressor (must be numeric). Default is 0.6.

na

is the number of points for computing the kernel (must be numeric). Default is 500.

logtransform

logical. If TRUE data are logtransformed prior to analysis as log(X+1). Default is FALSE.

interpolate

logical. If TRUE linear interpolation is applied to produce a timeseries of equal length as the original. Default is FALSE (assumes there are no gaps in the timeseries).

Value

ddjnonparam_ews returns an object with elements:

avec

is the mesh for which values of the nonparametric statistics are estimated.

S2.vec

is the conditional variance of the timeseries x over avec.

TotVar.dx.vec

is the total variance of dx over avec.

Diff2.vec

is the diffusion estimated as total variance - jumping intensity vs avec.

LamdaZ.vec

is the jump intensity over avec.

Tvec1

is the timeindex.

S2.t

is the conditional variance of the timeseries x data over Tvec1.

TotVar.t

is the total variance of dx over Tvec1.

Diff2.t

is the diffusion over Tvec1.

Lamda.t

is the jump intensity over Tvec1.

In addition, ddjnonparam_ews returns a first plot with the original timeseries and the residuals after first-differencing. A second plot shows the nonparametric conditional variance, total variance, diffusion and jump intensity over the data, and a third plot the same nonparametric statistics over time.

Details

The approach is based on estimating terms of a drift-diffusion-jump model as a surrogate for the unknown true data generating process: [1] $dx = f(x,\theta)dt + g(x,\theta)dW + dJ$ Here x is the state variable, f() and g() are nonlinear functions, dW is a Wiener process and dJ is a jump process. Jumps are large, one-step, positive or negative shocks that are uncorrelated in time.

Arguments:

References

Carpenter, S. R. and W. A. Brock (2011). 'Early warnings of unknown nonlinear shifts: a nonparametric approach.' Ecology 92(12): 2196-2201

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

See Also

generic_ews; ddjnonparam_ews; bdstest_ews; sensitivity_ews;surrogates_ews; ch_ews; movpotential_ews; livpotential_ews

Examples

data(foldbif)
output<-ddjnonparam_ews(foldbif,bandwidth=0.6,na=500,
logtransform=TRUE,interpolate=FALSE)