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)

Arguments

an autoregressive time series.

method

the method to be used by mcp or scad. See plus in R packages plus for details.

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.

Value

pluscpv 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.

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

# NOT RUN {
### 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<t<769 Y(t)=1.32Y(t-1)-0.81Y(t-2)+e(t), if 769<t<1024


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 3: Six change points with sample size 10000###
n <- 10000
Y <- rnorm(n)
cp1 <- c(3, 1427, 3084, 4394, 5913, 7422, 8804, 10000)

a1 <- c(1.58, 1.12, 1.61, 1.24, 1.53, 1.32, 1.69)
a2 <- c(-0.79, -0.68, -0.75, -0.66, -0.64, -0.81, -0.81)

for (j in 2:length(cp1)) {
  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)


mcp.cp <- cpvnts(Y, "mcp", 4, 0.01)
mcp.cp  #result of AMCP

scad.cp <- cpvnts(Y, "scad", 4, 0.01)
scad.cp  #result of ASCAD


# }