# Multiscale MOSUM algorithm with bottom-up merging Multiscale MOSUM procedure with symmetric bandwidths combined with bottom-up bandwidth-based merging. ```r 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 ```r 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. . 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.

multiscale.bottomUp function