Change Point Confidence Intervals

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+1000)
confidence_interval(X,changes = 100)
#>   change lower upper
#> 1    100   100   100
confidence_interval(X,changes=100,method = 'simulation')
#>   change lower upper
#> 1    100   100   100

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)
#>   change    lower    upper
#> 1    100 90.18279 111.0141
confidence_interval(X,changes=100,alpha = 0.1,method = 'simulation')
#>   change    lower    upper
#> 1    100 89.86422 110.2641

X <- generate_brownian_motion(200,v=seq(0,1,0.05))
confidence_interval(X,100)
#>   change     lower    upper
#> 1    100 -212.4403 450.5309
confidence_interval(X,100,method = 'simulation')
#>   change     lower    upper
#> 1    100 -230.9607 422.3643

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))
#>   change     lower    upper
#> 1    200 -33.89291 462.4076
#> 2    300 184.66503 429.3958

confidence_interval(X = electricity, changes = c(64, 120),alpha = 0.1)
#>   change     lower     upper
#> 1     64  44.51625  85.85908
#> 2    120 116.84947 123.53462