MultiWindow {offlineChange}

Multi-window Change Points Detection

Description

Use a sequence of window sizes to capture ranges of change points.

Usage

MultiWindow(
  y,
  window_list = c(100, 50, 20, 10, 5),
  point_max = 5,
  prior_range = NULL,
  get_mle = GetMle,
  penalty = "bic",
  seg_min = 1,
  num_init = NULL,
  tolerance = 1,
  cpp = TRUE,
  ret_score = FALSE
)

Arguments

y

The original data to find change points. Must be one dimensional data

window_list

The list of window sizes, must be in form c(100,50,20,10,5), in descending order and each window_size > 2L. L is the lag order of the dataset.

point_max

The largest candidate number of change points.

prior_range

The prior ranges that considered to contain change points.Each prior range contains one change point. example: prior_range=list(c(30,200),c(220,400))

get_mle

The method used to transform dependent data to independent data.

penalty

Penalty type term. Default is "bic". Users can use other penalty term.

seg_min

Minimal segment size between change points at transformed sacle, must be positive integer.

num_init

The number of repetition times, in order to avoid local minimum. Default is squared root of number of transformed data.

tolerance

The tolerance level. The maximal difference between the score of selected peak ranges and highest score.

cpp

Logical value indicating whether to accelerate using rcpp. Default is TRUE.

ret_score

Logical value indicating whether to return score. Default is FALSE.

Details

Given time series data y1,y2...yN, a sequence of window sizes w1 > ... > wR can be used to capture any true segment of small size. For each wr, the original data is turned into a sequence of L + 1 dimensional data that can be approximated as independent. Then the change points of independent data can be detected by minimizing penalized quadratic loss. By further mapping these change points back to the original scale, several short ranges (each of size 2wr) that probably contain the desired change points are obtained. After repeating the above procedure for different wr, the detected ranges of change points from each window size are scored by one. The scores are aggregated, and the ranges with highest score or around the highest score (determined by the tolerance parameter) are finally selected.

Value

n_peak_range

The number of peak ranges.

peak_ranges

The location of peak ranges.

score

score matrix. (only when ret_score is TRUE)

References

J. Ding, Y. Xiang, L. Shen, and V. Tarokh, Multiple Change Point Analysis: Fast Implementation and Strong Consistency. IEEE Transactions on Signal Processing, vol. 65, no. 17, pp. 4495-4510, 2017.

Examples

N <- 1000
N1 <- floor(0.1*N)
N2 <- floor(0.3*N)
a1 <- c(0.8, -0.3); c1 <- 0
a2 <- c(-0.5, 0.1); c2 <- 0
a3 <- c(0.5, -0.5); c3 <- 0
y <- rep(0,N)
L<-2
y[1:L] <- rnorm(L)
for (n in (L+1):N){
  if (n <= N1) {
    y[n] <- y[(n-1):(n-L)] %*% a1 + c1 + rnorm(1)
  } else if (n <= (N1+N2)) {
    y[n] <- y[(n-1):(n-L)] %*% a2 + c2 + rnorm(1)
  }
  else {
    y[n] <- y[(n-1):(n-L)] %*% a3 + c3 + rnorm(1)
  }
}
MultiWindow(y,window_list=c(100,50,20,10,5),point_max=5)
MultiWindow(y,window_list=c(100,50,20,10,5),prior_range=list(c(30,200),c(220,400)))