Tri_Mid_n1: Calculation of candidates, restricted for faster estimation...
In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

Description Usage Arguments Details Value Author(s) References See Also Examples

This function calculates candidates for estimates by simplicial depth based on intersections from residual straights. Thereby for large samples the candidates can be restricted by quantiles to reduce computational costs. Further points at the centroid of the candidate simplexes are calculated and the non-linear model without intercept is considered.

1	Tri_Mid_n1(y, perc, candy)

`y`	A series form from a non-linear AR(1) process for which the candidates have to be calculated.
`perc`	A value between 0 and 1 defining what range of candidates around of their median has to be considered for the optimisation. A value close to 0 gives a low precision, while a value of 1 evaluates all candidates.
`candy`	This is a switch, which decides, if the candidates shall be restricted to the edges of the respective simplices `candy = FALSE` or if in addition interior points shall be evaluated `candy = TRUE`.

The main idea for the candidate construction is presented in Kustosz (2016).

The returned value is a matrix of candidate parameters whereby the first column is θ_1 and the second θ_2.

Kustosz, Christoph

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

est_nlin1, dS_lin2_test

set.seed(17)
y <- RandomARMod_nlin1(nobs = 20, arp = 0.001, power = 1.001, start = 15, cont = "0")
par(mfrow = c(1, 2))
tt1 <- Tri_Mid_n1(y = y, perc = 0.5, candy = FALSE)
plot(tt1[,1], tt1[,2])
tt2 <- Tri_Mid_n1(y = y, perc = 0.5, candy = TRUE)
plot(tt2[,1], tt2[,2])