confidence_interval: Change Point Confidence Intervals

In fChange: Functional Change Point Detection and Analysis

Change Point Confidence Intervals

Description

Compute confidence intervals for the data based on some changes. The current version is tuned to mean changes.

Usage

confidence_interval(
  X,
  changes,
  K = bartlett_kernel,
  h = 2 * ncol(X)^(1/5),
  weighting = 0.5,
  M = 5000,
  alpha = 0.1,
  method = "distribution"
)

Arguments

X	A dfts object or data which can be automatically converted to that format. See dfts().
changes	Numeric vector for detected change points.
K	Function for the Kernel. Default is bartlett_kernel.
h	Numeric for bandwidth in computation of long run variance. The default is 2N^{1/5}.
weighting	Weighting for the interval computation, value in [0,1]. Default is 0.5.
M	Numeric for the number of Brownian motion simulations in computation of the confidence interval. Default is 1000.
alpha	Numeric for the significance level, in [0,1]. Default is 0.1.
method	String to indicate the method for computing the percentiles used in the confidence intervals. The options are 'distribution' and 'simulation'. Default is 'distribution'.

Value

Data.frame with the first column for the changes, second for the lower bounds of confidence intervals, and the third for the upper bounds of confidence intervals.

References

Horvath, L., & Rice, G. (2024). Change Point Analysis for Time Series (First edition.). Springer.

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.

Examples

X <- cbind(
  generate_brownian_motion(100, v = seq(0, 1, 0.05))$data,
  generate_brownian_motion(100, v = seq(0, 1, 0.05))$data + 0.5
)
confidence_interval(X, 100, alpha = 0.1)
confidence_interval(X, changes = 100, alpha = 0.1, method = "simulation")

X <- generate_brownian_motion(200, v = seq(0, 1, 0.05))
confidence_interval(X, 100)
confidence_interval(X, 100, method = "simulation")

X <- cbind(
  generate_brownian_motion(200, v = seq(0, 1, 0.05))$data,
  generate_brownian_motion(100, v = seq(0, 1, 0.05))$data + 0.1,
  generate_brownian_motion(150, v = seq(0, 1, 0.05))$data - 0.05
)
confidence_interval(X, c(200, 300))

confidence_interval(X = electricity, changes = c(64, 120), alpha = 0.1)

fChange documentation built on June 21, 2025, 9:08 a.m.