cpvnts: Multiple change point detection and variable selection for nonstationary time series models.

Description

This function provides a novel and fast methodology for simultaneous multiple structural break estimation and variable selection for nonstationary time series models by using ASCAD or AMCP to estimate the chang-points proposed by Jin, Shi and Wu (2011).

Usage

cpvnts(Y, method = c("mcp", "scad"), p, lam.d)

Value

cpvnts returns an object of class "cpvnts". An object of class "cpvnts" is a list containing the following components:

variable.selection: a matrix of variable selection. Element of the matrix is 1 if the variable is selected and 0 otherwise.
change.points: estimators of change points.

Arguments

Y: an autoregressive time series.
method: the method to be used by mcp or scad. See ncvreg in R packages ncvreg for details.
p: an upper bound of autoregressive orders.
lam.d: an parameter of the refining procedure. Suggest lam.d=0.05 if the length of Y is smaller than 5000 and lam.d=0.01 otherwise.

References

Jin, B., Shi, X., and Wu, Y. (2013). A novel and fast methodology for simultaneous multiple structural break estimation and variable selection for nonstationary time series models. Statistics and Computing, 23(2), 221-231.

Examples

Run this code

### Example 1: No change point with sample size 1000###

n <- 1000
Y <- rnorm(n)
cp1 <- c(3, 1000)
a0 <- c(0.7)
a1 <- c(1.3)
a2 <- c(-0.8)

for (j in 2:2) {
  for (i in (cp1[j - 1] + 1):cp1[j]) {
    Y[i] <- a0[j - 1] + a1[j - 1] * Y[i - 1] + a2[j - 1] * Y[i - 2] +
      rnorm(1)
  }
}

ts.plot(Y)

# Y(t)=0.7+1.3Y(t-1)-0.8Y(t-2)+e(t)


mcp.cp <- cpvnts(Y, "mcp", 4, 0.05)
mcp.cp  #result of AMCP

scad.cp <- cpvnts(Y, "scad", 4, 0.05)
scad.cp  #result of ASCAD


### Example 2(Davis et al (2006)):Two change points with sample size
### 1024##
n <- 1024
Y <- rnorm(n)
cp1 <- c(3, 512, 769, 1024)
a1 <- c(0.9, 1.69, 1.32)
a2 <- c(0, -0.81, -0.81)

for (j in 2:4) {
  for (i in (cp1[j - 1] + 1):cp1[j]) {
    Y[i] <- a1[j - 1] * Y[i - 1] + a2[j - 1] * Y[i - 2] + rnorm(1)
  }
}

ts.plot(Y)

# Y(t)=0.9Y(t-1)+e(t),if t<512 Y(t)=1.69Y(t-1)-0.81Y(t-2)+e(t), if
# 512