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Type:

Package

Title:

Nonparametric Change Point Detection for Multivariate Time Series

Version:

0.3.0

Depends:

R (≥ 4.1.0)

Maintainer:

Euan T. McGonigle <e.t.mcgonigle@soton.ac.uk>

License:

GPL (≥ 3)

Description:

Implements the nonparametric moving sum procedure for detecting changes in the joint characteristic function (NP-MOJO) for multiple change point detection in multivariate time series. See McGonigle, E. T., Cho, H. (2025) <doi:10.1093/biomet/asaf024> for description of the NP-MOJO methodology.

Encoding:

UTF-8

LinkingTo:

Rcpp

Imports:

Rcpp, doParallel, parallel, parallelly, foreach, Rfast, iterators, stats

URL:

https://github.com/EuanMcGonigle/CptNonPar

BugReports:

https://github.com/EuanMcGonigle/CptNonPar/issues

RoxygenNote:

7.3.2

Suggests:

covr, testthat (≥ 3.0.0)

Config/testthat/edition:

NeedsCompilation:

yes

Packaged:

2025-04-16 14:05:12 UTC; euanmcgonigle

Author:

Euan T. McGonigle [aut, cre], Haeran Cho [aut]

Repository:

CRAN

Date/Publication:

2025-04-16 14:30:21 UTC

CptNonPar: Nonparametric Change Point Detection for Multivariate Time Series

Description

Implements the nonparametric moving sum procedure for detecting changes in the joint characteristic function (NP-MOJO) for multiple change point detection in multivariate time series. See McGonigle, E. T., Cho, H. (2025) doi:10.1093/biomet/asaf024 for description of the NP-MOJO methodology.

Author(s)

Maintainer: Euan T. McGonigle e.t.mcgonigle@soton.ac.uk

Authors:

Haeran Cho haeran.cho@bristol.ac.uk

Examples

set.seed(1)
n <- 500
noise <- c(rep(1, 300), rep(0.4, 200)) * stats::arima.sim(model = list(ar = 0.3), n = n)
signal <- c(rep(0, 100), rep(2, 400))
x <- signal + noise
x.c <- np.mojo.multilag(x, G = 83, lags = c(0, 1))
x.c$cpts
x.c$cpt.clusters

Merge Change Point Estimators from Multiple Lags

Description

Merges change point estimators from different lagged values into a final set of overall change point estimators.

Usage

multilag.cpts.merge(
  x.c,
  eta.merge = 1,
  merge.type = c("sequential", "bottom-up")[1]
)

Arguments

x.c

A list object, where each element of the list is the output of the np.mojo function computed at a different lag.

eta.merge

A positive numeric value for the minimal mutual distance of changes, relative to bandwidth, used to merge change point estimators across different lags.

merge.type

String indicating the method used to merge change point estimators from different lags. Possible choices are

"sequential": starting from the left-most change point estimator and proceeding forward in time, estimators are grouped into clusters based on mutual distance. The estimator yielding the largest corresponding importance score is chosen as the change point estimator for that cluster. See McGonigle and Cho (2025) for details.
"bottom-up": starting with the largest importance score, the change points are merged using bottom-up merging (Messer et al. (2014)).

Details

See McGonigle and Cho (2025) for further details.

Value

A list object which contains the following fields

cpts

A matrix with rows corresponding to final change point estimators, with estimated change point location and associated lag and importance score given in columns.

cpt.clusters

A list object of length given by the number of detected change points. Each field contains a matrix of all change point estimators that are declared to be associated to the corresponding change point in the cpts field.

References

McGonigle, E.T., Cho, H. (2025). Nonparametric data segmentation in multivariate time series via joint characteristic functions. Biometrika (to appear).

Messer M., Kirchner M., Schiemann J., Roeper J., Neininger R., Schneider G. (2014). A Multiple Filter Test for the Detection of Rate Changes in Renewal Processes with Varying Variance. The Annals of Applied Statistics, 8(4), 2027-2067.

Examples

set.seed(1)
n <- 500
noise <- c(rep(1, 300), rep(0.4, 200)) * stats::arima.sim(model = list(ar = 0.3), n = n)
signal <- c(rep(0, 100), rep(2, 400))
x <- signal + noise
x.c0 <- np.mojo(x, G = 83, lag = 0)
x.c1 <- np.mojo(x, G = 83, lag = 1)
x.c <- multilag.cpts.merge(list(x.c0, x.c1))
x.c

Multiscale Nonparametric Multiple Lag Change Point Detection

Description

For a given set of bandwidths and lagged values of the time series, performs multiscale nonparametric change point detection of a possibly multivariate time series.

Usage

multiscale.np.mojo(
  x,
  G,
  lags = c(0, 1),
  kernel.f = c("quad.exp", "gauss", "euclidean", "laplace", "sine")[1],
  kern.par = 1,
  data.driven.kern.par = TRUE,
  threshold = c("bootstrap", "manual")[1],
  threshold.val = NULL,
  alpha = 0.1,
  reps = 200,
  boot.dep = 1.5 * (nrow(as.matrix(x))^(1/3)),
  parallel = FALSE,
  boot.method = c("mean.subtract", "no.mean.subtract")[1],
  criterion = c("eta", "epsilon", "eta.and.epsilon")[3],
  eta = 0.4,
  epsilon = 0.02,
  use.mean = FALSE,
  eta.merge = 1,
  merge.type = c("sequential", "bottom-up")[1],
  eta.bottom.up = 0.8
)

Arguments

x

Input data (a numeric vector or an object of classes ts and timeSeries, or a numeric matrix with rows representing observations and columns representing variables).

G

A numeric vector containing the moving sum bandwidths; all values in the vector G should be less than half the length of the time series.

lags

A numeric vector giving the range of lagged values of the time series that will be used to detect changes. See np.mojo.multilag for further details.

kernel.f

String indicating which kernel function to use when calculating the NP-MOJO detector statistics; with kern.par = a, possible values are

"quad.exp": kernel h_2 in McGonigle and Cho (2025), kernel 5 in Fan et al. (2017):

h (x,y) = \prod_{i=1}^{2p} \frac{ (2a - (x_i - y_i)^2) \exp (-\frac{1}{4a} (x_i - y_i)^2 )}{2a} .
"gauss": kernel h_1 in McGonigle and Cho (2025), the standard Gaussian kernel:

h (x,y) = \exp ( - \frac{a^2}{2} \Vert x - y \Vert^2).
"euclidean": kernel h_3 in McGonigle and Cho (2025), the Euclidean distance-based kernel:

h (x, y ) = \Vert x - y \Vert^a .
"laplace": kernel 2 in Fan et al. (2017), based on a Laplace weight function:

h (x, y ) = \prod_{i=1}^{2p} \left( 1+ a^2 (x_i - y_i)^2 \right)^{-1}.
"sine": kernel 4 in Fan et al. (2017), based on a sinusoidal weight function:

h (x, y ) = \prod_{i=1}^{2p} \frac{-2 | x_i - y_i | + | x_i - y_i - 2a| + | x_i - y_i +2a| }{4a} .

kern.par

The tuning parameter that appears in the expression for the kernel function, which acts as a scaling parameter.

data.driven.kern.par

A logical variable, if set to TRUE, then the kernel tuning parameter is calculated using the median heuristic, if FALSE it is given by kern.par.

threshold

String indicating how the threshold is computed. Possible values are

"bootstrap": the threshold is calculated using the bootstrap method with significance level alpha.
"manual": the threshold is set by the user and must be specified using the threshold.val parameter.

threshold.val

The value of the threshold used to declare change points, only to be used if threshold = "manual". Can be either a single numeric value, in which case the same threshold is used for all bandwidths and lags, or a list of vectors, with the length of the list equal to the number of bandwidths, that corresponds to the G argument, where the elements of each vector in the list corresponds to the threshold value for the corresponding element of the lags argument.

alpha

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

reps

An integer value for the number of bootstrap replications performed, if threshold = "bootstrap".

boot.dep

A positive value for the strength of dependence in the multiplier bootstrap sequence, if threshold = "bootstrap".

parallel

A logical variable, if set to TRUE, then parallel computing is used in the bootstrapping procedure if bootstrapping is performed.

boot.method

A string indicating the method for creating bootstrap replications. It is not recommended to change this. Possible choices are

"mean.subtract": the default choice, as described in McGonigle and Cho (2025). Empirical mean subtraction is performed to the bootstrapped replicates, improving power.
"no.mean.subtract": empirical mean subtraction is not performed, improving size control.

criterion

String indicating how to determine whether each point k at which NP-MOJO statistic exceeds the threshold is a change point; possible values are

"epsilon": k is the maximum of its local exceeding environment, which has at least size epsilon*G.
"eta": there is no larger exceeding in an eta*G environment of k.
"eta.and.epsilon": the recommended default option; k satisfies both the eta and epsilon criterion. Recommended to use with the standard value of eta that would be used if criterion = "eta" (e.g. 0.4), but much smaller value of epsilon than would be used if criterion = "epsilon", e.g. 0.02.

eta

A positive numeric value for the minimal mutual distance of changes, relative to bandwidth (if criterion = "eta" or criterion = "eta.and.epsilon").

epsilon

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

use.mean

Logical variable, only to be used if data.drive.kern.par=TRUE. If set to TRUE, the mean of pairwise distances is used to set the kernel function tuning parameter, instead of the median. May be useful for binary data, not recommended to be used otherwise.

eta.merge

A positive numeric value for the minimal mutual distance of changes, relative to bandwidth, used to merge change point estimators across different lags.

merge.type

String indicating the method used to merge change point estimators from different lags. Possible choices are

"sequential": Starting from the left-most change point estimator and proceeding forward in time, estimators are grouped into clusters based on mutual distance. The estimator yielding the largest corresponding importance score is chosen as the change point estimator for that cluster. See McGonigle and Cho (2025) for details.
"bottom-up": starting with the largest importance score, the change points are merged using bottom-up merging (Messer et al. (2014)).

eta.bottom.up

A positive numeric value for the minimal mutual distance of changes, relative to bandwidth, for use in bottom-up merging of change point estimators across multiple bandwidths.

Details

The multi-lag NP-MOJO algorithm for nonparametric change point detection is described in McGonigle, E. T. and Cho, H. (2025) Nonparametric data segmentation in multivariate time series via joint characteristic functions. Biometrika (to appear). The multiscale version uses bottom-up merging to combine the results of the multi-lag NP-MOJO algorithm performed over a given set of bandwidths.

Value

A list object that contains the following fields:

G

Set of moving window bandwidths

lags

Lags used to detect changes

kernel.f, data.driven.kern.par, use.mean

Input parameters

threshold, alpha, reps, boot.dep, boot.method, parallel

Input parameters

criterion, eta, epsilon

Input parameters

cpts

A matrix with rows corresponding to final change point estimators, with estimated change point location and associated detection bandwidth, lag and importance score given in columns.

References

McGonigle, E.T., Cho, H. (2025). Nonparametric data segmentation in multivariate time series via joint characteristic functions. Biometrika (to appear).

Fan, Y., de Micheaux, P.L., Penev, S. and Salopek, D. (2017). Multivariate nonparametric test of independence. Journal of Multivariate Analysis, 153, pp.189-210.

Examples

set.seed(1)
n <- 500
noise <- c(rep(1, 300), rep(0.4, 200)) * stats::arima.sim(model = list(ar = 0.3), n = n)
signal <- c(rep(0, 100), rep(2, 400))
x <- signal + noise
x.c <- multiscale.np.mojo(x, G = c(50, 80), lags = c(0, 1))
x.c$cpts

Nonparametric Single Lag Change Point Detection

Description

For a given lagged value of the time series, performs nonparametric change point detection of a possibly multivariate time series. If lag \ell = 0, then only marginal changes are detected. If lag \ell \neq 0, then changes in the pairwise distribution of (X_t , X_{t+\ell}) are detected.

Usage

np.mojo(
  x,
  G,
  lag = 0,
  kernel.f = c("quad.exp", "gauss", "euclidean", "laplace", "sine")[1],
  kern.par = 1,
  data.driven.kern.par = TRUE,
  alpha = 0.1,
  threshold = c("bootstrap", "manual")[1],
  threshold.val = NULL,
  reps = 200,
  boot.dep = 1.5 * (nrow(as.matrix(x))^(1/3)),
  parallel = FALSE,
  boot.method = c("mean.subtract", "no.mean.subtract")[1],
  criterion = c("eta", "epsilon", "eta.and.epsilon")[3],
  eta = 0.4,
  epsilon = 0.02,
  use.mean = FALSE
)

Arguments

x

Input data (a numeric vector or an object of classes ts and timeSeries, or a numeric matrix with rows representing observations and columns representing variables).

G

An integer value for the moving sum bandwidth; G should be less than half the length of the time series.

lag

The lagged values of the time series used to detect changes. If lag \ell = 0, then only marginal changes are detected. If lag \ell \neq 0, then changes in the pairwise distribution of (X_t , X_{t+\ell}) are detected.

kernel.f

String indicating which kernel function to use when calculating the NP-MOJO detectors statistics; with kern.par = a, possible values are

"quad.exp": kernel h_2 in McGonigle and Cho (2025), kernel 5 in Fan et al. (2017):

h (x,y) = \prod_{i=1}^{2p} \frac{ (2a - (x_i - y_i)^2) \exp (-\frac{1}{4a} (x_i - y_i)^2 )}{2a} .
"gauss": kernel h_1 in McGonigle and Cho (2025), the standard Gaussian kernel:

h (x,y) = \exp ( - \frac{a^2}{2} \Vert x - y \Vert^2) .
"euclidean": kernel h_3 in McGonigle and Cho (2025), the Euclidean distance-based kernel:

h (x, y ) = \Vert x - y \Vert^a .
"laplace": kernel 2 in Fan et al. (2017), based on a Laplace weight function:

h (x, y ) = \prod_{i=1}^{2p} \left( 1+ a^2 (x_i - y_i)^2 \right)^{-1}.
"sine": kernel 4 in Fan et al. (2017), based on a sinusoidal weight function:

h (x, y ) = \prod_{i=1}^{2p} \frac{-2 | x_i - y_i | + | x_i - y_i - 2a| + | x_i - y_i +2a| }{4a} .

kern.par

The tuning parameter that appears in the expression for the kernel function, which acts as a scaling parameter, only to be used if data.driven.kern.par = FALSE. If kernel.f = "euclidean", then kern.par \in (0,2), otherwise kern.par > 0.

data.driven.kern.par

A logical variable, if set to TRUE, then the kernel tuning parameter is calculated using the median heuristic, if FALSE it is given by kern.par.

alpha

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

threshold

String indicating how the threshold is computed. Possible values are

"bootstrap": the threshold is calculated using the bootstrap method with significance level alpha.
"manual": the threshold is set by the user and must be specified using the threshold.val parameter.

threshold.val

The value of the threshold used to declare change points, only to be used if threshold = "manual".

reps

An integer value for the number of bootstrap replications performed, if threshold = "bootstrap".

boot.dep

A positive value for the strength of dependence in the multiplier bootstrap sequence, if threshold = "bootstrap".

parallel

A logical variable, if set to TRUE, then parallel computing is used in the bootstrapping procedure if bootstrapping is performed.

boot.method

A string indicating the method for creating bootstrap replications. It is not recommended to change this. Possible choices are

"mean.subtract": the default choice, as described in McGonigle and Cho (2025). Empirical mean subtraction is performed to the bootstrapped replicates, improving power.
"no.mean.subtract": empirical mean subtraction is not performed, improving size control.

criterion

String indicating how to determine whether each point k at which NP-MOJO statistic exceeds the threshold is a change point; possible values are

"epsilon": k is the maximum of its local exceeding environment, which has at least size epsilon*G.
"eta": there is no larger exceeding in an eta*G environment of k.
"eta.and.epsilon": the recommended default option; k satisfies both the eta and epsilon criterion. Recommended to use with the standard value of eta that would be used if criterion = "eta" (e.g. 0.4), but much smaller value of epsilon than would be used if criterion = "epsilon", e.g. 0.02.

eta

A positive numeric value for the minimal mutual distance of changes, relative to bandwidth (if criterion = "eta" or criterion = "eta.and.epsilon").

epsilon

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

use.mean

Logical variable, only to be used if data.drive.kern.par=TRUE. If set to TRUE, the mean of pairwise distances is used to set the kernel function tuning parameter, instead of the median. May be useful for binary data, not recommended to be used otherwise.

Details

The single-lag NP-MOJO algorithm for nonparametric change point detection is described in McGonigle, E. T. and Cho, H. (2025) Nonparametric data segmentation in multivariate time series via joint characteristic functions. Biometrika (to appear).

Value

A list object that contains the following fields:

x

Input data

G

Moving window bandwidth

lag

Lag used to detect changes

kernel.f, data.driven.kern.par, use.mean

Input parameters

kern.par

The value of the kernel tuning parameter

threshold, alpha, reps, boot.dep, boot.method, parallel

Input parameters

threshold.val

Threshold value for declaring change points

criterion, eta, epsilon

Input parameters

test.stat

A vector containing the NP-MOJO detector statistics computed from the input data

cpts

A vector containing the estimated change point locations

scores

The corresponding importance scores of the estimated change points. The larger the score is, the more likely that there exists a change point close to the estimated location. If the bootstrap method is used, this a value between 0 and 1 corresponding to the proportion of times the observed detector statistic was larger than the bootstrapped detector statistics. Otherwise, the importance score is simply the value of the detector statistic at the estimated change point location (which is not necessarily less than 1).

References

McGonigle, E.T., Cho, H. (2025). Nonparametric data segmentation in multivariate time series via joint characteristic functions. Biometrika (to appear).

Fan, Y., de Micheaux, P.L., Penev, S. and Salopek, D. (2017). Multivariate nonparametric test of independence. Journal of Multivariate Analysis, 153, pp.189-210.

Examples

set.seed(1)
n <- 500
noise <- c(rep(1, 300), rep(0.4, 200)) * stats::arima.sim(model = list(ar = 0.3), n = n)
signal <- c(rep(0, 100), rep(2, 400))
x <- signal + noise
x.c <- np.mojo(x, G = 83, lag = 0)
x.c$cpts
x.c$scores

Nonparametric Multiple Lag Change Point Detection

Description

For a given set of lagged values of the time series, performs nonparametric change point detection of a possibly multivariate time series.

Usage

np.mojo.multilag(
  x,
  G,
  lags = c(0, 1),
  kernel.f = c("quad.exp", "gauss", "euclidean", "laplace", "sine")[1],
  kern.par = 1,
  data.driven.kern.par = TRUE,
  threshold = c("bootstrap", "manual")[1],
  threshold.val = NULL,
  alpha = 0.1,
  reps = 200,
  boot.dep = 1.5 * (nrow(as.matrix(x))^(1/3)),
  parallel = FALSE,
  boot.method = c("mean.subtract", "no.mean.subtract")[1],
  criterion = c("eta", "epsilon", "eta.and.epsilon")[3],
  eta = 0.4,
  epsilon = 0.02,
  use.mean = FALSE,
  eta.merge = 1,
  merge.type = c("sequential", "bottom-up")[1]
)

Arguments

x

Input data (a numeric vector or an object of classes ts and timeSeries, or a numeric matrix with rows representing observations and columns representing variables).

G

An integer value for the moving sum bandwidth; G should be less than half the length of the time series.

lags

A numeric vector giving the range of lagged values of the time series that will be used to detect changes. See np.mojo for further details.

kernel.f

String indicating which kernel function to use when calculating the NP-MOJO detector statistics; with kern.par = a, possible values are

"quad.exp": kernel h_2 in McGonigle and Cho (2025), kernel 5 in Fan et al. (2017):

h (x,y) = \prod_{i=1}^{2p} \frac{ (2a - (x_i - y_i)^2) \exp (-\frac{1}{4a} (x_i - y_i)^2 )}{2a} .
"gauss": kernel h_1 in McGonigle and Cho (2025), the standard Gaussian kernel:

h (x,y) = \exp ( - \frac{a^2}{2} \Vert x - y \Vert^2) .
"euclidean": kernel h_3 in McGonigle and Cho (2025), the Euclidean distance-based kernel:

h (x, y ) = \Vert x - y \Vert^a .
"laplace": kernel 2 in Fan et al. (2017), based on a Laplace weight function:

h (x, y ) = \prod_{i=1}^{2p} \left( 1+ a^2 (x_i - y_i)^2 \right)^{-1}.
"sine": kernel 4 in Fan et al. (2017), based on a sinusoidal weight function:

h (x, y ) = \prod_{i=1}^{2p} \frac{-2 | x_i - y_i | + | x_i - y_i - 2a| + | x_i - y_i +2a| }{4a} .

kern.par

The tuning parameter that appears in the expression for the kernel function, which acts as a scaling parameter.

data.driven.kern.par

A logical variable, if set to TRUE, then the kernel tuning parameter is calculated using the median heuristic, if FALSE it is given by kern.par.

threshold

String indicating how the threshold is computed. Possible values are

"bootstrap": the threshold is calculated using the bootstrap method with significance level alpha.
"manual": the threshold is set by the user and must be specified using the threshold.val parameter.

threshold.val

The value of the threshold used to declare change points, only to be used if threshold = "manual". Can be either a single numeric value, in which case the same threshold is used for all lags, or a vector with length equal to the number of lags, where each elements in the vector gives the threshold value of the corresponding lag from the lags argument.

alpha

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

reps

An integer value for the number of bootstrap replications performed, if threshold = "bootstrap".

boot.dep

A positive value for the strength of dependence in the multiplier bootstrap sequence, if threshold = "bootstrap".

parallel

A logical variable, if set to TRUE, then parallel computing is used in the bootstrapping procedure if bootstrapping is performed.

boot.method

A string indicating the method for creating bootstrap replications. It is not recommended to change this. Possible choices are

"mean.subtract": the default choice, as described in McGonigle and Cho (2025). Empirical mean subtraction is performed to the bootstrapped replicates, improving power.
"no.mean.subtract": empirical mean subtraction is not performed, improving size control.

criterion

String indicating how to determine whether each point k at which NP-MOJO statistic exceeds the threshold is a change point; possible values are

"epsilon": k is the maximum of its local exceeding environment, which has at least size epsilon*G.
"eta": there is no larger exceeding in an eta*G environment of k.
"eta.and.epsilon": the recommended default option; k satisfies both the eta and epsilon criterion. Recommended to use with the standard value of eta that would be used if criterion = "eta" (e.g. 0.4), but much smaller value of epsilon than would be used if criterion = "epsilon", e.g. 0.02.

eta

A positive numeric value for the minimal mutual distance of changes, relative to bandwidth (if criterion = "eta" or criterion = "eta.and.epsilon").

epsilon

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

use.mean

eta.merge

A positive numeric value for the minimal mutual distance of changes, relative to bandwidth, used to merge change point estimators across different lags.

merge.type

String indicating the method used to merge change point estimators from different lags. Possible choices are

"sequential": Starting from the left-most change point estimator and proceeding forward in time, estimators are grouped into clusters based on mutual distance. The estimator yielding the largest corresponding importance score is chosen as the change point estimator for that cluster. See McGonigle and Cho (2025) for details.
"bottom-up": starting with the largest importance score, the change points are merged using bottom-up merging (Messer et al. (2014)).

Details

Value

A list object that contains the following fields:

G

Moving window bandwidth

lags

Lags used to detect changes

kernel.f, data.driven.kern.par, use.mean

Input parameters

threshold, alpha, reps, boot.dep, boot.method, parallel

Input parameters

criterion, eta, epsilon

Input parameters

cpts

A matrix with rows corresponding to final change point estimators, with estimated change point location and associated lag and importance score given in columns.

cpt.clusters

References

McGonigle, E.T., Cho, H. (2025). Nonparametric data segmentation in multivariate time series via joint characteristic functions. Biometrika (to appear).

Fan, Y., de Micheaux, P.L., Penev, S. and Salopek, D. (2017). Multivariate nonparametric test of independence. Journal of Multivariate Analysis, 153, pp.189-210.

Examples

set.seed(1)
n <- 500
noise <- c(rep(1, 300), rep(0.4, 200)) * stats::arima.sim(model = list(ar = 0.3), n = n)
signal <- c(rep(0, 100), rep(2, 400))
x <- signal + noise
x.c <- np.mojo.multilag(x, G = 83, lags = c(0, 1))
x.c$cpts
x.c$cpt.clusters

CptNonPar: Nonparametric Change Point Detection for Multivariate Time Series

Description

Author(s)

See Also

Examples

Merge Change Point Estimators from Multiple Lags

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Multiscale Nonparametric Multiple Lag Change Point Detection

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Nonparametric Single Lag Change Point Detection

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Nonparametric Multiple Lag Change Point Detection

Description

Usage

Arguments

Details

Value

References

See Also

Examples