changepoint (version 1.1.5)

single.var.css: Single Change in Variance - Cumulative Sums of Squares

Description

Calculates the cumulative sums of squares (css) test statistic for all possible changepoint locations and returns the single most probable (max).

Usage

single.var.css(data,penalty="SIC",pen.value=0,class=TRUE,param.estimates=TRUE)

Arguments

data

A vector, ts object or matrix containing the data within which you wish to find a changepoint. If data is a matrix, each row is considered a separate dataset.

penalty

Choice of "None", "SIC", "BIC", "AIC", "Hannan-Quinn", "Asymptotic" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. If Asymptotic is specified, the theoretical type I error is contained in the p

pen.value

The theoretical type I error e.g.0.05 when using the Asymptotic penalty (options are 0.01,0.05,0.1,0.25,0.5,0.75,0.9,0.95). The value of the penalty when using the Manual penalty option. This can be a numeric value or text giving the formula to use. Av

class

Logical. If TRUE then an object of class cpt is returned. If FALSE a vector is returned.

param.estimates

Logical. If TRUE and class=TRUE then parameter estimates are returned. If FALSE or class=FALSE no parameter estimates are returned.

Value

• If class=TRUE then an object of S4 class "cpt" is returned. The slot cpts contains the changepoints that are solely returned if class=FALSE. The structure of cpts is as follows.

  If data is a vector (single dataset) then a single value is returned:

• cpt
  The most probable location of a changepoint if H0 was rejected or NA if H1 was rejected.
• If data is an mxn matrix (multiple datasets) then a vector is returned:
• cpt
  Vector of length m containing where each element is the result of the test for data[m,]. If cpt[m] is a number then it is the most probable location of a changepoint under H1. Otherwise cpt[m] has the value NA and indicates that H1 was rejected.

Details

This function is used to find a single change in variance for data that is is not assumed to follow a specific distribtuion. The value returned is the result of testing H0:no change in variance against H1: single change in variance using the cumulative sums of squares test statistic coupled with the penalty supplied.

References

C. Inclan, G. C. Tiao (1994) Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance, Journal of the American Statistical Association 89(427), 913--923

R. L. Brown, J. Durbin, J. M. Evans (1975) Techniques for Testing the Constancy of Regression Relationships over Time, Journal of the Royal Statistical Society B 32(2), 149--192

See Also

cpt.var,cpt

Examples

# Example of a change in variance at 100 in simulated normal data
set.seed(1)
x=c(rnorm(100,0,1),rnorm(100,0,10))
single.var.css(x,penalty="Asymptotic",pen.value=0.05,class=FALSE) # returns 105 to show that the
#null hypothesis was rejected and the change in variance is at 105
ans=single.var.css(x,penalty="Asymptotic",pen.value=0.01) 
cpts(ans) # returns 105 to show that the null hypothesis was rejected, the change in variance is at
#105 and we are 99% confident of this result

# Example of a data matrix containing 2 rows, row 1 has a change in variance and row 2 had no change
#in variance
set.seed(10)
x=c(rnorm(100,0,1),rnorm(100,0,10))
y=rnorm(200,0,1)
z=rbind(x,y)
single.var.css(z,penalty="Asymptotic",pen.value=0.05,class=FALSE) # returns vector c(102,200) which
#shows that the first dataset has a change in variance at 102 and the second dataset rejected H1 and
#has no change in variance
ans=single.var.css(z,penalty="Manual",pen.value=2) 
cpts(ans[[1]]) # test using a manual penalty which is the same as the AIC penalty for this example
cpts(ans[[2]]) # result is the same as above, c(102, 200)