GetMleAr {offlineChange}

Estimate Coefficients using ar Function

Description

Transform N dependent data into approximated independent data (N/window_size) x (L+1). Computes the estimated coefficients of each window of original data.

Usage

GetMleAr(y, window_size)

Arguments

y

The original data to find change points.

window_size

The number of observations each window contains.

Value

x

The transformed data, which are the estimated coefficients of original data.

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)
  }
}
GetMleAr(y,window_size=100)