dS3_nlin2: dS3 for the non-linear AR(1) model with intercept

In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

Description

This function calculates a simplified version of simplicial depth for explosive AR(1) processes, when overlapping residuals are evaluated. Thereby the parameter theta and the process y are fixed. The assumed model is given by

Y_n = Y_{n-1}+θ_1 *Y_{n-1}^{θ_2} + θ_0 +E_n,

whereby E_n i.i.d. errors with med(E_n) = 0.

Usage

dS3_nlin2(theta, y)

Arguments

theta	θ = (θ_1,θ_2,θ_0), parameter vector to evaluate dS1 in.
y	y = (y_0,...,y_N), oberserved process to evaluate dS1 in.

Details

The theoretical details can be found in Kustosz, Mueller 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., Mueller 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_nlin2(nobs = 100, intercept = 0, arp = 0.2, power = 1.01, start = 15, cont = "0")
theta <- c(0.2, 1.01, 0)
dS3_nlin2(theta, y)
dS3_nlin2(theta+0.1, y)

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