multiscale.localPrune: Multiscale MOSUM algorithm with localised pruning

In mosum: Moving Sum Based Procedures for Changes in the Mean

Multiscale MOSUM algorithm with localised pruning

Description

Multiscale MOSUM procedure with (possibly) assymetric bandwidths and localised pruning based on Schwarz criterion.

Usage

multiscale.localPrune(
  x,
  G = bandwidths.default(length(x)),
  max.unbalance = 4,
  threshold = c("critical.value", "custom")[1],
  alpha = 0.1,
  threshold.function = NULL,
  criterion = c("eta", "epsilon")[1],
  eta = 0.4,
  epsilon = 0.2,
  rule = c("pval", "jump")[1],
  penalty = c("log", "polynomial")[1],
  pen.exp = 1.01,
  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 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). Asymmetric bandwidths obtained as the Cartesian product of the set G with itself are used for change point analysis
max.unbalance	a numeric value for the maximal ratio between maximal and minimal bandwidths to be used for candidate generation, 1 <= max.unbalance <= Inf
threshold	string indicating which threshold should be used to determine significance. By default, it is chosen from the asymptotic distribution at the 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_l, G_r, length(x), alpha), to compute a threshold of significance for different bandwidths (G_l, G_r); use iff threshold = "custom"
criterion	how to determine whether an exceeding point is a change point; to be parsed to mosum
eta, epsilon	see mosum
rule	string for the choice of sorting criterion for change point candidates in merging step. Possible values are: "pval"smallest p-value "jump"largest (rescaled) jump size
penalty	string specifying the type of penalty term to be used in Schwarz criterion; possible values are: "log"use penalty = log(length(x))^pen.exp "polynomial"use penalty = length(x)^pen.exp
pen.exp	exponent for the penalty term (see penalty);
do.confint	flag indicating whether confidence intervals for change points should be computed
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 parsed to mosum calls

Details

See Algorithm 2 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
sc	Schwarz criterion values of the estimated change point set
pooled.cpts	set of change point candidates that have been considered by the algorithm
G	input parameter
threshold, alpha, threshold.function	input parameters
criterion, eta, epsilon	input parameters
rule, penalty, pen.exp	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>.

H. Cho and C. Kirch (2022) Two-stage data segmentation permitting multiscale change points, heavy tails and dependence. Annals of the Institute of Statistical Mathematics, Volume 74, Number 4, pp. 653-684.

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

x <- testData(model = "mix", seed = 123)$x
mlp <- multiscale.localPrune(x, G = c(8, 15, 30, 70), do.confint = TRUE)
print(mlp)
summary(mlp)
par(mfcol=c(2, 1), mar = c(2, 4, 2, 2))
plot(mlp, display = "data", shaded = "none")
plot(mlp, display = "significance", shaded = "CI", CI = "unif")

mosum documentation built on Oct. 22, 2022, 5:05 p.m.