lin2_CI_cl: Confidence regions for linar AR(1) processes with intercept...
In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

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

This function generates confidence regions for linear AR(1) processes with intercept and explosion based on simplified and full simplicial depth for AR processes. This is a version which uses a predefined cluster. This allows a calculation of the confidence sets on HPC's.

1	lin2_CI_cl(y, level, plots = FALSE, notion = "dS1", cluster, eps = 1e-19)

`y`	A observed series from an linear AR(1) process with intercept.
`level`	A value in (0,1) defining the level of the confidence regions to evaluate.
`plots`	A swich to turn on and off plots of the resulting region. Use `plots = TRUE` to turn on plots and `plots = FALSE` (default) to suppress plotting.
`notion`	A parameter to select the desired depth notion to evaluate. The possible choices are "dS1", "dS2", "dS3" and "dS" defining three simplified notions as discussed in Kustosz, Mueller and Wendler (2016) and the full depth discussed in Kustosz, Leucht and Mueller (2016). The standard notion is "dS1".
`cluster`	Initialised cluster for parallel computation.
`eps`	Parameter to shift the candidates to differ from parameters defined by roots of residuals.

The theoretical details can be found in Kustosz, Mueeller and Wendler (2016) and Kustosz, Leucht and Mueller (2016). The details on the implementation are in Kustosz (2016).

`par`	A matrix with the evaluated points to calculate the confidence region by evaluation of the depth tests.
`inCI`	A binary vector indicating, if a parameter in par is in the confidence interval or not. Thereby the test decision is reported. Hence, `inCI = 0` donotes a parameter being inside of the confidence set and `inCI = 1` denotes a parameter which is not.

Kustosz, Christoph

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.

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.

dS1_lin2_test,dS2_lin2_test,dS3_lin2_test,dS_lin2_test,lin2_theta_f,convex_hull_plot

y1 <- RandomARMod_lin2(50, 0.2, 1.002, 15, "0")

## Not run: 
cl <- makeCluster(2)
A1 <- lin2_CI_cl(y1, 0.95, notion = "dS1", cluster = cl)
A2 <- lin2_CI_cl(y1, 0.95, notion = "dS2", cluster = cl)
A3 <- lin2_CI_cl(y1, 0.95, notion = "dS3", cluster = cl)
AS <- lin2_CI_cl(y1, 0.95, notion = "dS", cluster = cl)
ASp <- lin2_CI_cl(y1, 0.95, notion = "dS_pre", cluster = cl)

stopCluster(cl)

par(mfrow=c(2, 2))
plot(AS$par[AS$inCI == 0, ], col = 3, pch = 19, main = "dS vs dSp")
points(ASp$par[ASp$inCI == 0, ], col = 2)
plot(A1$par[!A1$inCI, ], col = 2, pch = 19, main = "dS1 vs dS")
points(AS$par[!AS$inCI, ], col = 3)
plot(A2$par[!A2$inCI, ], col = 2, pch = 19, main = "dS2 vs dS")
points(AS$par[!AS$inCI, ], col = 3)
plot(A3$par[!A3$inCI, ], col = 2, pch = 19, main = "dS3 vs dS")
points(AS$par[!AS$inCI, ], col = 3)

## End(Not run)