mosum {mosum}

MOSUM procedure for multiple change point estimation

Description

Computes the MOSUM detector, detects (multiple) change points and estimates their locations.

Usage

mosum(
  x,
  G,
  G.right = G,
  var.est.method = c("mosum", "mosum.min", "mosum.max", "custom")[1],
  var.custom = NULL,
  boundary.extension = TRUE,
  threshold = c("critical.value", "custom")[1],
  alpha = 0.1,
  threshold.custom = NULL,
  criterion = c("eta", "epsilon")[1],
  eta = 0.4,
  epsilon = 0.2,
  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

an integer value for the moving sum bandwidth; G should be less than length(n)/2. Alternatively, a number between 0 and 0.5 describing the moving sum bandwidth relative to length(x) can be given

G.right

if G.right != G, the asymmetric bandwidth (G, G.right) will be used; if max(G, G.right)/min(G, G.right) > 4, a warning message is generated

var.est.method

how the variance is estimated; possible values are

• "mosum"both-sided MOSUM variance estimator

• "mosum.min"minimum of the sample variance estimates from the left and right summation windows

• "mosum.max"maximum of the sample variance estimates from the left and right summation windows

• "custom"a vector of length(x) is to be parsed by the user; use var.custom in this case to do so

var.custom

a numeric vector (of the same length as x) containing local estimates of the variance or long run variance; use iff var.est.method = "custom"

boundary.extension

a logical value indicating whether the boundary values should be filled-up with CUSUM values

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 numerical value with threshold.custom

alpha

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

threshold.custom

a numeric value greater than 0 for the threshold of significance; use iff threshold = "custom"

criterion

string indicating how to determine whether each point k at which MOSUM statistic exceeds the threshold is a change point; possible values are

• "eta"there is no larger exceeding in an eta*G environment of k

• "epsilon"k is the maximum of its local exceeding environment, which has at least size epsilon*G

eta

a positive numeric value for the minimal mutual distance of changes, relative to moving sum bandwidth (iff criterion = "eta")

epsilon

a numeric value in (0,1] for the minimal size of exceeding environments, relative to moving sum bandwidth (iff criterion = "epsilon")

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

Value

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

x

input data

G.left, G.right

left and right summation bandwidths

var.est.method, var.custom, boundary.extension

input parameters

stat

a series of MOSUM statistic values; the first G and last G.right values are NA iff boundary.extension = FALSE

rollsums

a series of MOSUM detector values; equals stat*sqrt(var.estimation)

var.estimation

the local variance estimated according to var.est.method

threshold, alpha, threshold.custom

input parameters

threshold.value

threshold value of the corresponding MOSUM test

criterion, eta, epsilon

input parameters

cpts

a vector containing the estimated change point locations

cpts.info

data frame containing information about change point estimators including detection bandwidths, asymptotic p-values for the corresponding MOSUM statistics and (scaled) size of jumps

do.confint

input parameter

ci

S3 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>.

B. Eichinger and C. Kirch (2018) A MOSUM procedure for the estimation of multiple random change-points. Bernoulli, Volume 24, Number 1, pp. 526-564.

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(lengths = rep(100, 3), means = c(0, 5, -2), sds = rep(1, 3), seed = 1234)$x
m <- mosum(x, G = 40)
plot(m)
summary(m)