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

Value

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

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.

See Also

ncvreg

Examples

### 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

Two stage multiple change point detection in linear models.

Description

This function provides a two‐stage procedure for simultaneously detecting multiple change‐points in linear models. In the cutting stage, the change‐point problem is converted into a model selection problem so that a modern model selection method can be applied. In the refining stage, the change‐points obtained in the cutting stage are finalized via a refining method. The tuning parameter lambda is chosen by BIC.

Usage

tsmcplm(Y, X, method = c("lasso", "adapt", "mcp", "scad"), c)

Arguments

Value

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

References

Jin, B., Wu, Y., & Shi, X. (2016). Consistent two‐stage multiple change‐point detection in linear models. Canadian Journal of Statistics, 44(2), 161-179.

See Also

ncvreg lars

Examples

## example 1 : mean shift model
## true change point location:
## 100, 130, 150, 230, 250, 400, 440, 650, 760, 780, 810
Y <- rnorm(1000, 0, 0.5) +
  c(rep(0,100), rep(4,30),rep(-1,20), rep(2,80), rep(-2,20),
    rep(3,150), rep(-1, 40), rep(1,210), rep(5,110), rep(2,20),
    rep(7,30), rep(3,190))
ts.plot(Y)

##estimate change points
tsmcplm(Y = Y, X = NULL, method = "adapt", c = 0.3)


## example 2: linear model:
## a periodic auto correlation series with period 122 and
## order of auto correlation 1

###
## true change point location:
## 200, 350, 450, 550, 700, and 850


n=1000
y <- rnorm(n)
for (t in 2:n) {
  y[t] <- cos(t*pi/61) + 3*sin(t*pi/61) + 0.5*y[t-1] + (2*sin(t*pi/61) +
  0.1 * y[t-1])*(200 < t)+ (2* cos(t*pi/61) - 4 *sin(t*pi/61) -
  0.6* y[t-1] )*(350 < t) + (2* sin(t*pi/61) +
  0.7* y[t-1] )*(450 < t) + (-3* sin(t*pi/61) -
  0.3* y[t-1] )*(550 < t) + (-3* cos(t*pi/61) +
  5* sin(t*pi/61))* (700 < t) + (3* cos(t*pi/61) -
  5* sin(t*pi/61) - 0.4*y[t-1] )* (850 < t) + rnorm(1)
}
ts.plot(y)

x <- sapply(2:n, function(t){cbind(cos(t*pi/61), sin(t*pi/61), y[t-1])}, simplify = FALSE)
x <- do.call(rbind, x)
tsmcplm(Y = y[-1], X = x, method = "adapt", c = 2)