dS_lin2: Simplicial depth for explosive AR(1) processes

In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

Description

This function calculates simplicial depth for explosive AR(1) processes as defined in Kustosz, Mueller and Leucht (2016). Thereby it is capable to autodetects the number of available cores or uses a user defined number of cores to speed up computation. The basic model is defined by

Y_n = θ_0 + θ_1 Y_ {n-1}+E_n

, with Y_n being an increasing process and E_n satisfying med(E_n) = 0.

Usage

dS_lin2(theta, resy, y, ncores = 1,
model = c("linAR1", "nlinAR1", "linARc"), cpow = 1)

Arguments

theta	Parameter θ for which simplicial depth has to be evaluated. Thereby the dimension of the parameter is defined by the selected model.
resy	Here residuals of an arbitrary model with two parameter can be inserted, instead of defining a parameter theta and y, to evaluate depth directly on the signs of these residuals.
y	Observed proces y=(y_0,...,y_N) for which simplicial depth has to be evaluated.
ncores	Number of cores for parallel computation. If no value is selected the method sets the cores to 1 and no parallel comutation is applied. If the value is set to 'auto', the function detects the available number of cores and uses the maximal number minus 1. The function produces errors, if more cores than available or a wrong argument is inserted.
model	Here the model for the calculation of the underlying residuals is specified. currently the following models are available "linAR1" = linear AR(1) model with intercept Y_n = θ_1 Y_{n-1} θ_0 + E_n "nlinAR1" = linear AR(1) model without intercept but with power parameter Y_n = Y_{n-1} + θ_1 Y_{n-1}^{θ_3} + E_n "linARc" = linear AR(1) model with intercept and fixed and knwon power cpow Y_n = θ_1 Y_{n-1}^{cpow} + θ_0 + E_n
cpow	Fixed and known power parameter for the Y_n = θ_1*Y_{n-1}^{cpow} + θ_0 model.

Details

The theoretical details can be found in Kustosz, Leucht and Mueller (2016). The computational details are in Kustosz (2016).

Value

The function returns the simplicial depth of the parameter theta for an observed process y.

Note

The function depends on several internal functions.

Author(s)

Christoph Kustosz and Sebastian Szugat

References

Kustosz, C. (2016). Depth based estimators and tests for autoregressive processes with application. Ph. D. thesis. TU Dortmund.

Kustosz C., Leucht A. and Mueller Ch. H. (2016). Tests based on simplicial depth for AR(1) models with explosion. Journal of Time Series Analysis. In press.

See Also

resARMod_lin2, dS_lin2,dS1_lin2, dS2_lin2, dS3_lin2, oner

Examples

y <- RandomARMod_lin2(100, 0.2, 1.01, 15, "0")
theta <- c(0.2, 1.01)
dS_lin2(theta = theta, y = y)
dS_lin2(theta = theta + 0.1, y = y)

ChrisKust/rexpar documentation built on May 6, 2019, 11:48 a.m.