dS2_lin2_sym: dS for AR(1) with two parameters in a symmetrised version

In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

Description

This function calculates the simplicial depth for explosive AR(1) processes with two parameters. Thereby the parameter θ and the process y are fixed. The assumed model given by the argument model. Further the kernel is replaced by a symmetrised version. This in particular allows the application of standard limit theorems for U-Statistics.

Usage

dS_lin2_sym(theta, resy, y, ncores = 1, 
model = c("linAR1", "nlinAR1", "linARc"), cpow = 1)

Arguments

theta	θ, parameter (vector) to evaluate dS1 in.
resy	Instead of a model and a parameter theta, residuals can be plugged in directly. Then just the sign changes are calculated and the statistic is evaluated
y	y = (y_0,...,y_N), oberserved process to evaluate dS1 in.
ncores	This value allows the usage of multiple cores to calculate the statistic
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) = theta2*y(n)^cpow + theta1 model

Details

The theoretical details can be found in Kustosz, M\"uller and Wendler (2016). The computational details are in Kustosz (2016).

Value

Result is a real number which gives the depth of theta based on the obervation y.

Note

This expression is a simplification of dS, which is the full simplicial depth for explosive AR(1) processes

Author(s)

Kustosz, Christoph

References

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

Kustosz C., M\"uller Ch. H. and Wendler M. (2016). Simplified Simplicial Depth for Regression and Autoregressive Growth Processes. Journal of Statistical Planning and Inference. In press.

See Also

resARMod_lin2, dS_lin2,dS1_lin2, dS2_lin2, dS3_lin2

Examples

y <- RandomARMod_lin2(100, 0.2, 1.01, 15, "0")
theta <- c(0.2, 1.01)
dS_lin2_sym(theta = theta, y = y, model = "linAR1")
dS_lin2_sym(theta = theta+0.1, y = y, model = "linAR1")

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