Change Point Detection — fchange • fChange

Change point detection for dfts objects. Various change point methods are given, where single or multiple changes can be detected. Multiple change extensions currently include binary segmentation and elbow plots.

Usage

fchange(
  X,
  method = c("characteristic", "mean", "robustmean", "eigenjoint", "eigensingle",
    "trace", "covariance", "projmean", "projdistribution"),
  statistic = c("Tn", "Mn"),
  critical = c("simulation", "resample", "welch"),
  type = c("single", "segmentation", "elbow"),
  resample_blocks = "separate",
  replace = TRUE,
  max_changes = min(ncol(X), 20),
  changes = NULL,
  blocksize = 2 * ncol(X)^(1/5),
  eigen_number = 3,
  h = 2 * ncol(X)^(1/5),
  M = 1000,
  J = 50,
  W = space_measuring_functions(X = X, M = 20, space = "BM"),
  K = bartlett_kernel,
  alpha = 0.05,
  cov.res = 30,
  weighting = 1/4,
  TVE = 0.95,
  trim_function = function(X) {
     0
 },
  errors = "L2",
  recommendation_change_points = 2,
  recommendation_improvement = 0.15,
  silent.binary = FALSE
)

Arguments

X: A dfts object or data which can be automatically converted to that format. See dfts().
method: Method to compute change point. Options include: 'characteristic', 'mean', 'robustmean', 'eigenjoint', 'eigensingle', 'trace', 'covariance', 'projmean', and 'projdistribution'.
statistic: String for the test statistic type: integrated, Tn, or supremum, Mn.
critical: String for method of computing threshold. Options are 'simulation', 'resample', and 'welch'. Not all ways to compute the critical thresholds are implemented for every method.
type: String for the type of change point detection, single change ('single'), binary segmentation ('segmentation'), or elbow plots ('elbow').
resample_blocks: String indicating the type of resample test to use. Using separate gives blocks which are separate while overlapping creates overlapping or sliding windows. When blocksize=1 then these will be identical.
replace: Boolean for using a permutation or bootstrapped statistic when critical='resample'.
max_changes: Integer as the max number of changes to search when using type is elbow.
changes: Vector of change points to be given to the eigen test if the data should be centered on these values first.
blocksize: Integer for the width of the blocks when using a resampling test. Can use adaptive_bandwidth() if additional guidance is desired.
eigen_number: Which eigenvalue or the number of eigenvalues which should be checked in the eigenvalue tests.
h: Number of lags used when computing long run covariance estimates. Used in mean, characteristic, and eigenvalue tests.
M: Number of simulations or permutations for critical values
J: Resolution (J) in the characteristic method. The number of vectors is defined by W.
W: Space measuring functions used in characteristic method to explore the functional space.
K: Kernel function for use in characteristic, mean, eigen, covariance and projmean.
alpha: Significance in [0,1] for Welch approximation.
cov.res: Resolution to use when computing covariance kernel changes.
weighting: Weights used in covariance kernel method and pcadistribution.
TVE: Total variance explained for projmean and projdistribution.
trim_function: Trimming to be used in multiple change methods.
errors: Type of errors used in elbow plot. Options are L2 and Trace.
recommendation_change_points: Number of lags forward to examine in deciding automated elbow plot recommendation.
recommendation_improvement: Significant drop to look for in deciding automated elbow plot recommendation.
silent.binary: Boolean if output should be printed when running binary segmentation.

Value

When type is single, returns a list:

pvalue: p-value for detection of a change point.
location: location of the most likely change.

When type is elbow:

information: data.frame with the information on each change and the decrease in variability.
plots: list of plots showing the variability decrease or improvement
suggestion: list with plot and algorithmic change suggestion. The suggested changes are also returned.

When type is segmentation a data.frame with the locations and p-values is returned.

References

Aue, A., Rice, G., & Sonmez, O. (2018). Detecting and dating structural breaks in functional data without dimension reduction. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 80(3), 509-529.

Wegner, L., Wendler, M. Robust change-point detection for functional time series based on U-statistics and dependent wild bootstrap. Stat Papers (2024).

Aue, A., Rice, G., & Sonmez, O. (2020). Structural break analysis for spectrum and trace of covariance operators. Environmetrics (London, Ont.), 31(1)

Horvath, L., Rice, G., & Zhao, Y. (2022). Change point analysis of covariance functions: A weighted cumulative sum approach. Journal of Multivariate Analysis, 189, 104877-.

Berkes, I., Gabrys, R.,Horvath, L. & P. Kokoszka (2009)., Detecting changes in the mean of functional observations Journal of the Royal Statistical Society, Series B 71, 927-946

Aue, A., Gabrys, R.,Horvath, L. & P. Kokoszka (2009)., Estimation of a change-point in the mean function of functional data Journal of Multivariate Analysis 100, 2254-2269.

Huskova, M., & Meintanis, S.G. (2006). Change Point Analysis based on Empirical Characteristic Functions. Metrika, 63, 145-168.

Examples

res <- fchange(electricity$data[,1:20],method='characteristic',critical = 'welch')