changepoints_lin2_cl: Change-point detection for a linear AR(1) model with...
In ChrisKust/rexpar: Simplicial Depth for Explosive Autoregressive Processes

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

This function detects change points for parameter changes of a linear AR(1) model with intercept based on simplicial depth. The model is defined by

Y_n = θ_1 Y_{n-1} + θ_0 + E_n

with med(E_n)=0. The main idea is based on estimators and confidence intervals based on simplicial depth as proposed by Kustosz (2016). Further, a preselection of candidates by a simplified depth notion is used. This is a version which uses a preset cluster which hast to be passed as argument when calling the function.

1	changepoints_lin2_cl(y, level, bw, sw, plots, method, cluster, mincper, mincp)

`y`	An observed AR(1) process with intercept.
`level`	The level for which the confidence intervals for the phase change detection are calculated.
`bw`	A bandwidth defining the sample size for sub-samples which are evaluated in the detection algorithm.
`sw`	A step-width to reduce the candidate points in which the change points are evaluated.
`plots`	A switch (TRUE and FALSE) to determine if plots shall be produced for each tested candidate
`method`	This parameter determines the method to detect change points. If `method = "m1"` is selected a candidate is marked as change, if the confidence intervals do not overlap. For `method = "m2"` the change point is marked, if the estimates are not inside of the non respective confidence intervals.
`cluster`	Initialized cluster for parallel computing.
`mincper`	Percentage to define relevant change-point clusters based on the length of the 'mincp' longest detected cluster.
`mincp`	The 'mincp' longest cluster is used to define a threshold for detected clusters which are considered for final break-point estimates. This implies, that (if enough clusters exist), the number also defines the minimal amount of detected breakpoints.

For details see Kustosz (2016).

`candidates`	A vector of observation indices in which the algorithm tested for change points.
`changepoints`	A vector indicating, if a change point was detected in the respective candidate.

Kustosz, Christoph

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

RandomARMod_lin2, lin2_CI_cl, convex_hull_plot, convex_hull_intersect, est_lin2, dS_lin2, dS_lin2_test, dS1_lin2_test

int1 <- 0.1
int2 <- 0.3
arp1 <- 1.015
arp2 <- 1.001

set.seed(123)
y1 <- RandomARMod_lin2(50, int1, arp1, 15, "0")
y2 <- RandomARMod_lin2(50, int2, arp2, y1[length(y1)], "0")
y <- c(y1,y2)





## Not run: 
cl <- makeCluster(2)

CP1 <- changepoints_lin2_cl(y, 0.99, 25, 5, plots = FALSE, method = "m1", cl = cl)
CP2 <- changepoints_lin2_cl(y, 0.99, 25, 5, plots = FALSE, method = "m2", cl = cl)


stopCluster(cl)

par(mfrow = c(2, 1))
plot(y, type="l")
abline(v=CP1$candidates[CP1$changepoints==1], col=4,lty=4)
abline(v=CP2$candidates[CP2$changepoints==1], col=5,lty=5)

plot(y, type="l")
abline(v=CP1$rjumps, col=4,lty=4,lwd=2)
abline(v=CP2$rjumps, col=5,lty=5,lwd=3)

## End(Not run)