multiscale.localPrune {mosum}

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")