multiscale.bottomUp function

Multiscale MOSUM algorithm with bottom-up merging

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

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

Returns

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

Details

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

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)

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.