Default choice for the set of multiple bandwidths

Description

Create bandwidths according to a default function of the sample size

Usage

bandwidths.default(n, d.min = 10, G.min = 10, G.max = min(n/2, n^(2/3)))

Arguments

Details

Returns an integer vector of bandwidths (G_1,...,G_m), with G_0 = G_1 = max(G.min, 2/3*d.min), G_j+1 = G_j-1 + G_j (for j = 1, ..., m-1) and m satisfying G_m <= G.max while G_m+1 > G.max.

Value

an integer vector of bandwidths

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.

Examples

bandwidths.default(1000, 10, 10, 200)

Obtain bootstrap replicate of time series

Description

Obtain bootstrap replicate of time series

Usage

bootstrapped_timeSeries(cpts, x)

Does the combination comb of changepoints contain the changepoint k_ind?

Description

Does the combination comb of changepoints contain the changepoint k_ind?

Usage

comb_contains_cpt(comb, k_ind)

Confidence intervals for change points

Description

Generate bootstrap confidence intervals for change points.

Usage

## S3 method for class 'mosum.cpts'
confint(object, parm = "cpts", level = 0.05, N_reps = 1000, ...)

Arguments

Details

See the referenced literature for further details

Value

S3 object of class cpts.ci, containing the following fields:

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) 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, 3, 1), sds = rep(1, 3), seed = 1337)$x
m <- mosum(x, G = 40)
ci <- confint(m, N_reps = 5000)
print(ci$CI)

Confidence intervals for change points

Description

Generate bootstrap confidence intervals for change points.

Usage

## S3 method for class 'multiscale.cpts'
confint(object, parm = "cpts", level = 0.05, N_reps = 1000, ...)

Arguments

Details

See the referenced literature for further details

Value

S3 object of class cpts.ci, containing the following fields:

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) 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, 3, 1), sds = rep(1, 3), seed = 1337)$x
mlp <-  multiscale.localPrune(x, G = c(8, 15, 30, 70))
ci <- confint(mlp, N_reps = 5000)
print(ci$CI)

Helping/wrapper fuction for C++ calls

Description

Helping/wrapper fuction for C++ calls

Usage

cpts_bootstrap(mcpts, N_reps, level)

Helping function to get bootstrap replicates of change point estimates

Description

Helping function to get bootstrap replicates of change point estimates

Usage

cpts_bootstrap_help(cpts_info, x, N_reps)

Final detection interval

Description

Final detection interval

Usage

detect.interval(all.cpts, est.cpts)

Remove duplicated from all.cpts data frame: In case one change being added multiple times, choose the one with smallest p-value

Description

Remove duplicated from all.cpts data frame: In case one change being added multiple times, choose the one with smallest p-value

Usage

dup.merge(all.cpts)

extract changepoints from candidates with eta criterion

Description

extract changepoints from candidates with eta criterion

Usage

eta_criterion_help(candidates, m_values, eta, G_left, G_right)

Algorithm II (Local change-point search with SC)

Description

Input cand: =mathcal D, conflicting changepoints candidate set Input sub_sums: Pre-computed partial sums, as obtained by extract_sub Input strength: Exponent for penalty Input log_penalty: log (or polynomial) penalty term? Input n: Overall length of data Input auc: =|mathcal C|, total number of currently active changepoints (+candidates) Input min_cost: Minimal RSS with all the candidates

Usage

exhaust_sc(cand, sub_sums, strength, log_penalty, n, auc, min_cost)

Details

Output sc: (Mx2) matrix (M=2^m with m=|cand|) containing RSS/cost and SC terms for all combinations within cand. Combinations are indexed by their implicit integer representation, i.e. sc[0,] corresponds to the empty set, sc[3,] to k_1,k_2 [0..011], etc. Note: Row May be Inf, if combination was not visited in algorithm. Output est_cpts: Integer Vector of estimated changepoints Output final: Bool Vector indicating if combinations are final states Output num_cpts: For debugging purposes

Helping function for algorithm 2: Pre-compute the partial sums S_i = sumj=k_i+1^k_i+1x_i and the partial sums of squared T_i = sumj=k_i+1^k_i+1x_i^2 between the (sorted) candidates k_i and k_i+1 in cand. Output: data frame with 4 columns k_i | k_i+1 | S_i | T_i

Description

Helping function for algorithm 2: Pre-compute the partial sums S_i = sumj=k_i+1^k_i+1x_i and the partial sums of squared T_i = sumj=k_i+1^k_i+1x_i^2 between the (sorted) candidates k_i and k_i+1 in cand. Output: data frame with 4 columns k_i | k_i+1 | S_i | T_i

Usage

extract_sub(cand, x)

Get integer vector of changepoint indices, based on bool-field representation of combinations. E.g. for combination index 11 [=1011]: get_comb_ind(c(T,F,T,T))=11

Description

Get integer vector of changepoint indices, based on bool-field representation of combinations. E.g. for combination index 11 [=1011]: get_comb_ind(c(T,F,T,T))=11

Usage

get_comb_ind(active)

Compute bootstrapped mosum statistic and return maximum position thereof

Description

Compute bootstrapped mosum statistic and return maximum position thereof

Usage

get_k_star(x_star, k_hat, G_l, G_r, G_ll, G_rr)

Compute the Local cost terms of combination icomb (for RSS resp. sBIC). Use pre-computed partial sum matrix sub_sums (see extract_sub) for speedup

Description

Compute the Local cost terms of combination icomb (for RSS resp. sBIC). Use pre-computed partial sum matrix sub_sums (see extract_sub) for speedup

Usage

get_local_costs(icomb, sub_sums)

Is index i_child a child of index i_parent? ASSERT: i_child is of the form (i_parent XOR i_help), with i_help having exactly one non-zero bit

Description

Is index i_child a child of index i_parent? ASSERT: i_child is of the form (i_parent XOR i_help), with i_help having exactly one non-zero bit

Usage

is_child(i_child, i_parent)

Identify the local environment for exhaustive search

Description

Identify the local environment for exhaustive search

Usage

local.env(j, est.cpts.ind, all.cpts, current, ac)

Localised pruning algorithm

Description

Localised pruning algorithm

Usage

local.prune(x, all.cpts, rule, log.penalty, pen.exp)

helping function for bootstrap (compute local means)

Description

helping function for bootstrap (compute local means)

Usage

mean_help(x, l, r)

Creating Time-Series according to example model

Description

Creates a time series according to the block model with independent innovations.

Usage

modelSignal.blocks(rand.gen = rnorm, ...)

Arguments

Details

See Appendix B in the reference for details about the signal model.

Value

a vector consisting of a realization of the signal model

References

P. Fryzlewicz (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, Volume 42, Number 6, pp. 2243-2281.

Creating Time-Series according to example model

Description

Creates a time series according to the block model with independent innovations.

Usage

modelSignal.fms(rand.gen = rnorm, ...)

Arguments

Details

See Appendix B in the reference for details about the signal model.

Value

a vector consisting of a realization of the signal model

References

P. Fryzlewicz (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, Volume 42, Number 6, pp. 2243-2281.

Creating Time-Series according to example model

Description

Creates a time series according to the block model with independent innovations.

Usage

modelSignal.mix(rand.gen = rnorm, ...)

Arguments

Details

See Appendix B in the reference for details about the signal model.

Value

a vector consisting of a realization of the signal model

References

P. Fryzlewicz (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, Volume 42, Number 6, pp. 2243-2281.

Creating Time-Series according to example model

Description

Creates a time series according to the block model with independent innovations.

Usage

modelSignal.stairs10(rand.gen = rnorm, ...)

Arguments

Details

See Appendix B in the reference for details about the signal model.

Value

a vector consisting of a realization of the signal model

References

P. Fryzlewicz (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, Volume 42, Number 6, pp. 2243-2281.

Creating Time-Series according to example model

Description

Creates a time series according to the block model with independent innovations.

Usage

modelSignal.teeth10(rand.gen = rnorm, ...)

Arguments

Details

See Appendix B in the reference for details about the signal model.

Value

a vector consisting of a realization of the signal model

References

P. Fryzlewicz (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, Volume 42, Number 6, pp. 2243-2281.

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

Value

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

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)

Help function: asymptotic scaling.

Description

Help function: asymptotic scaling.

Usage

mosum.asymptoticA(x)

Help function: asymptotic shift

Description

Help function: asymptotic shift

Usage

mosum.asymptoticB(x, K)

MOSUM asymptotic critical value

Description

Computes the asymptotic critical value for the MOSUM test.

Usage

mosum.criticalValue(n, G.left, G.right, alpha)

Arguments

Value

a numeric value for the asymptotic critical value for the MOSUM test

Examples

x <- testData(lengths = rep(100, 3), means = c(0, 5, -2), sds = rep(1, 3), seed = 1234)$x
m <- mosum(x, G = 40)
par(mfrow = c(2, 1))
plot(m$stat, type = "l", xlab = "Time", ylab = "", main = "mosum")
abline(h = mosum.criticalValue(300, 40, 40, .1), col = 4)
abline(v = m$cpts, col = 2)
plot(m, display = "mosum") # identical plot is produced 

MOSUM asymptotic p-value

Description

Computes the asymptotic p-value for the MOSUM test.

Usage

mosum.pValue(z, n, G.left, G.right = G.left)

Arguments

Value

a numeric value for the asymptotic p-value for the asymmetric MOSUM test

MOSUM statistic

Description

Computes the statistical values for the MOSUM test for changes in the mean.

Usage

mosum.stat(
  x,
  G,
  G.right = NA,
  var.est.method = "mosum",
  var.custom = NULL,
  boundary.extension = TRUE
)

Arguments

Details

This class only contains the values for the MOSUM statistic. For statistical evaluation and change point extraction, use mosum. See also multiscale.bottomUp and multiscale.localPrune.

Value

S3 mosum.stat object, which contains the following fields:

Multiscale MOSUM algorithm with bottom-up merging

Description

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

Usage

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

Details

See Algorithm 1 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:

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.

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)

Multiscale bandwidth grids

Description

Create asymmetric bandwidth grids to be used with multiscale.localPrune

Usage

multiscale.grid(
  bandwidths.left,
  bandwidths.right = bandwidths.left,
  method = "cartesian",
  max.unbalance = 4
)

Arguments

Value

S3 multiscale.grid object to be used in the multiscale.grid function

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

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:

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")

Next value to iterate (in lexicographical order) over all bit permutaions having l bits set to 1. Example sequence (2 bits): 0011, 0101, 0110, 1001, 1010, 1100. Source: https://stackoverflow.com/questions/1851134/generate-all-binary-strings-of-length-n-with-k-bits-set

Description

Next value to iterate (in lexicographical order) over all bit permutaions having l bits set to 1. Example sequence (2 bits): 0011, 0101, 0110, 1001, 1010, 1100. Source: https://stackoverflow.com/questions/1851134/generate-all-binary-strings-of-length-n-with-k-bits-set

Usage

next_bit_permutation(v)

Get number of non-zero bits of a 32bit integer Source: https://stackoverflow.com/questions/109023/how-to-count-the-number-of-set-bits-in-a-32-bit-integer

Description

Get number of non-zero bits of a 32bit integer Source: https://stackoverflow.com/questions/109023/how-to-count-the-number-of-set-bits-in-a-32-bit-integer

Usage

numberOfSetBits(i)

3D Visualisation of multiscale MOSUM statistics

Description

3D Visualisation of multiscale MOSUM statistics.

Usage

persp3D.multiscaleMosum(
  x,
  mosum.args = list(),
  threshold = c("critical.value", "custom")[1],
  alpha = 0.1,
  threshold.function = NULL,
  pal.name = "YlOrRd",
  expand = 0.2,
  theta = 120,
  phi = 20,
  xlab = "G",
  ylab = "time",
  zlab = "MOSUM",
  ticktype = "detailed",
  NAcol = "#800000FF",
  ...
)

Arguments

Details

The visualisation is based on persp3D. MOSUM statistics computed with different bandwidths are rescaled for making them visually comparable. Rescaling is done either by dividing by their respective critical value at the significance level alpha (iff threshold = "critical.value") or by a custom value given by threshold.function (iff threshold = "custom"). By default, clim argument of persp3D is given so that the three lightest (for sequential palettes) hues indicate insignificance of the corresponding MOSUM statistics, while darker hues indicate the presence of significant changes.

Value

see persp3D

Examples

## Not run: 
# If you run the example be aware that this may take some time
print("example may take some time to run")

x <- testData(model = "blocks", seed = 1234)$x
persp3D.multiscaleMosum(x, mosum.args = list(boundary.extension = FALSE))

## End(Not run)

Plotting the output from MOSUM procedure

Description

Plotting method for S3 objects of class mosum.cpts

Usage

## S3 method for class 'mosum.cpts'
plot(
  x,
  display = c("data", "mosum")[1],
  cpts.col = "red",
  critical.value.col = "blue",
  xlab = "Time",
  ...
)

Arguments

Details

The location of each change point estimator is plotted as a vertical line against the input time series and the estimated piecewise constant signal (display = "data") or MOSUM detector values (display = "mosum").

Examples

x <- testData(lengths = rep(100, 3), means = c(0, 5, -2), sds = rep(1, 3), seed = 1234)$x
m <- mosum(x, G = 40)
par(mfrow = c(2, 1), mar = c(2.5, 2.5, 2.5, .5))
plot(m, display = "data")
plot(m, display = "mosum")

Plotting MOSUM statistics

Description

Plotting method for objects of class 'mosum.stat'.

Usage

## S3 method for class 'mosum.stat'
plot(m, alpha = 0.05, critical.value.col = "blue", xlab = "Time", ...)

Arguments

Plotting the output from multiscale MOSUM procedure

Description

Plotting method for S3 objects of class "multiscale.cpts".

Usage

## S3 method for class 'multiscale.cpts'
plot(
  x,
  display = c("data", "significance")[1],
  shaded = c("CI", "bandwidth", "none")[1],
  level = 0.05,
  N_reps = 1000,
  CI = c("pw", "unif")[1],
  xlab = "Time",
  ...
)

Arguments

Details

The locations of change point estimators are plotted against the input time series and the estimated piecewise constant signal (display = "data"), or the significance of each estimator is represented by the corresponding 1-p.value derived from the asymptotic distribution of MOSUM test statistic (display = "significance"). It also produces the rectangles representing the detection intervals (if shaded = "bandwidth") or bootstrap confidence intervals of the corresponding change points (if shaded = "CI") around their locations.

Examples

x <- testData(model = "blocks", seed = 1234)$x
mlp <- multiscale.localPrune(x)
par(mfrow = c(2, 1))
plot(mlp, display = "data", shaded = "bandwidth")
plot(mlp, display = "significance", shaded = "CI")

Change points estimated by MOSUM procedure

Description

Print method for objects of class mosum.cpts

Usage

## S3 method for class 'mosum.cpts'
print(x, ...)

Arguments

Examples

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

Change points estimated by multiscale MOSUM procedure

Description

Print method for objects of class multiscale.cpts

Usage

## S3 method for class 'multiscale.cpts'
print(x, ...)

Arguments

Examples

x <- testData(model = "mix", seed = 12345)$x
mlp <- multiscale.localPrune(x)
print(mlp)

equivalent to rollsum(x, k=G, fill=NA, align="left") in the package zoo, but optimized for speed

Description

equivalent to rollsum(x, k=G, fill=NA, align="left") in the package zoo, but optimized for speed

Usage

rolling_sum(x, G)

where is leftmost one? https://www.geeksforgeeks.org/find-significant-set-bit-number/

Description

where is leftmost one? https://www.geeksforgeeks.org/find-significant-set-bit-number/

Usage

setBitNumber(n)

Starting value to iterate (in lexicographical order) over all bit permutaions having l bits set to 1. E.g.: start_bit_permutations(2) = 3 [=0..011].

Description

Starting value to iterate (in lexicographical order) over all bit permutaions having l bits set to 1. E.g.: start_bit_permutations(2) = 3 [=0..011].

Usage

start_bit_permutations(l)

Summary of change points estimated by MOSUM procedure

Description

Summary method for objects of class mosum.cpts

Usage

## S3 method for class 'mosum.cpts'
summary(object, ...)

Arguments

Details

Provide information about each estimated change point, including the bandwidths used for its estimation, associated p-value and (scaled) jump size; if object$do.confint=TRUE, end points of the pointwise and uniform confidence intervals are also provided.

Examples

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

Summary of change points estimated by multiscale MOSUM procedure

Description

Summary method for objects of class multiscale.cpts

Usage

## S3 method for class 'multiscale.cpts'
summary(object, ...)

Arguments

Details

Provide information about each estimated change point, including the bandwidths used for its detection, associated p-value and (scaled) jump size; if object$do.confint=TRUE, end points of the pointwise and uniform confidence intervals are also provided.

Examples

x <- testData(model = "mix", seed = 12345)$x
mlp <- multiscale.localPrune(x, do.confint = TRUE)
summary(mlp)

Test data with piecewise constant mean

Description

Generate piecewise stationary time series with independent innovations and change points in the mean.

Usage

testData(
  model = c("custom", "blocks", "fms", "mix", "stairs10", "teeth10")[1],
  lengths = NULL,
  means = NULL,
  sds = NULL,
  rand.gen = rnorm,
  seed = NULL,
  ...
)

Arguments

Details

See Appendix B in the reference for details about the test signals.

Value

a list containing the following entries:

• x a numeric vector containing a realisation of the piecewise time series model, given as signal + noise

• mu mean vector of piecewise stationary time series model

• sigma scaling vector of piecewise stationary time series model

• cpts a vector of change points in the piecewise stationary time series model

References

P. Fryzlewicz (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, Volume 42, Number 6, pp. 2243-2281.

Examples

# visualise estimated changepoints by solid vertical lines
# and true changepoints by broken vertical lines
td <- testData(lengths = c(50, 50, 200, 300, 300), means = c(0, 1, 2, 3, 2.3), 
sds = rep(1, 5), seed = 123)
mbu <- multiscale.bottomUp(td$x)
plot(mbu, display = "data")
abline(v = td$cpts, col = 2, lwd = 2, lty = 2)

# visualise estimated piecewise constant signal by solid line
# and true signal by broken line
td <- testData("blocks", seed = 123)
mlp <- multiscale.localPrune(td$x)
plot(mlp, display = "data")
lines(td$mu, col = 2, lwd = 2, lty = 2)

Piecewise constant test signal

Description

Produce vectors of mean and dispersion values for generating piecewise stationary time series.

Usage

testSignal(
  model = c("custom", "blocks", "fms", "mix", "stairs10", "teeth10")[1],
  lengths = NULL,
  means = NULL,
  sds = NULL
)

Arguments

Details

See Appendix B in the reference for details about the test signals.

Value

a list containing the following entries:

• mu_t mean vector of piecewise stationary model time series

• sigma_t deviation scaling vector of piecewise stationary model time series

References

P. Fryzlewicz (2014) Wild Binary Segmentation for Multiple Change-Point Detection. The Annals of Statistics, Volume 42, Number 6, pp. 2243-2281.