dS3_lin2: dS3 for AR(1) 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 θ and the process y are fixed. The assumed model given by the model defined by the model parameter.

Usage

dS3_lin2(theta, res, y, model = c("linAR1", "linAR1woI", "nlinAR1",
"linAR2", "linARc"), cpow = 1)

Arguments

theta	θ, parameter vector to evaluate dS3 in.
res	Here the evaluated residuals can be inserted, instead of a parameter theta and data y. Then the statistic is evaluated based on these residuals by calculation of their signs.
y	y = (y_0,...,y_N), oberserved process to evaluate dS3 in.
model	Here the model for the calculation of the underlying residuals is specified. currently the following models are available "linAR1woI" = linear AR(1) model without intercept Y_n = θ_1 Y_{n-1} + E_n "linAR1" = linear AR(1) model with intercept Y_n = θ_1 Y_{n-1} θ_0 + E_n "linAR2" = linear AR(2) model without intercept Y_n = θ_1 Y_{n-1} + θ_2 Y_{n-2} + 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, Mueller and Wendler (2016). The computational details are in Kustosz (2016).

Value

The 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)

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., 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_lin2(100, 0.02, 1.01, 15, "0")
theta <- c(0.02, 1.01)
dS3_lin2(theta = theta, y = y)
dS3_lin2(theta = theta + 0.1, y = y)

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