TSMCP (version 1.0)

tsmcplm: 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

Y

an response vector.

X

the n-by-p design matrix.

method

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

c

ceiling(c*sqrt(length(Y))) is the length of each segments in spliting stage.

Value

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

change.points

estimators of change points.

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

plus lars

Examples

# NOT RUN {
## 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)


# }