multiscale.bottomUp {mosum}

Multiscale MOSUM algorithm with bottom-up merging

Description

Multiscale MOSUM procedure with symmetric bandwidths combined with bottom-up bandwidth-based merging.

Usage

multiscale.bottomUp(
  x,
  G = bandwidths.default(length(x), G.min = max(20, ceiling(0.05 * length(x)))),
  threshold = c("critical.value", "custom")[1],
  alpha = 0.1,
  threshold.function = NULL,
  eta = 0.4,
  do.confint = FALSE,
  level = 0.05,
  N_reps = 1000,
  ...
)

Arguments

x

input data (a numeric vector or an object of classes ts and timeSeries)

G

a vector of (symmetric) bandwidths, given as either integers less than length(x)/2, or numbers between 0 and 0.5 describing the moving sum bandwidths relative to length(x). If the smallest bandwidth is smaller than min(20, 0.05*length(x)) (0.05 if relative bandwidths are given) and threshold = "critical.value", it generates a warning message

threshold

string indicating which threshold should be used to determine significance. By default, it is chosen from the asymptotic distribution at the given significance level alpha. Alternatively, it is possible to parse a user-defined function with threshold.function

alpha

a numeric value for the significance level with 0 <= alpha <= 1; use iff threshold = "critical.value"

threshold.function

function object of form function(G, length(x), alpha), to compute a threshold of significance for different bandwidths G; use iff threshold = "custom"

eta

see mosum

do.confint

flag indicating whether to compute the confidence intervals for change points

level

use iff do.confint = TRUE; a numeric value (0 <= level <= 1) with which 100(1-level)% confidence interval is generated

N_reps

use iff do.confint = TRUE; number of bootstrap replicates to be generated

...

further arguments to be passed to the mosum calls

Details

See Algorithm 1 in the first referenced paper for a comprehensive description of the procedure and further details.

Value

S3 object of class multiscale.cpts, which contains the following fields:

x

input data

cpts

estimated change points

cpts.info

data frame containing information about estimated change points

pooled.cpts

set of change point candidates that have been considered by the algorithm

G

bandwidths

threshold, alpha, threshold.function

input parameters

eta

input parameters

do.confint

input parameter

ci

object of class cpts.ci containing confidence intervals for change points iff do.confint = TRUE

References

A. Meier, C. Kirch and H. Cho (2021) mosum: A Package for Moving Sums in Change-point Analysis. Journal of Statistical Software, Volume 97, Number 8, pp. 1-42. <doi:10.18637/jss.v097.i08>.

M. Messer et al. (2014) A multiple filter test for the detection of rate changes in renewal processes with varying variance. The Annals of Applied Statistics, Volume 8, Number 4, pp. 2027-2067.

H. Cho and C. Kirch (2022) Bootstrap confidence intervals for multiple change points based on moving sum procedures. Computational Statistics & Data Analysis, Volume 175, pp. 107552.

Examples

x1 <- testData(lengths = c(100, 200, 300, 300), 
means = c(0, 1, 2, 2.7), sds = rep(1, 4), seed = 123)$x
mbu1 <- multiscale.bottomUp(x1)
plot(mbu1)
summary(mbu1)

x2 <- testData(model = "mix", seed = 1234)$x
threshold.custom <- function(G, n, alpha) {
mosum.criticalValue(n, G, G, alpha) * log(n/G)^0.1
}
mbu2 <- multiscale.bottomUp(x2, G = 10:40, threshold = "custom",
threshold.function = threshold.custom)
plot(mbu2)
summary(mbu2)