changepoint (version 1.1.5)

single.mean.cusum: Single Change in Mean - Cumulative Sums

Description

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

Usage

single.mean.cusum(data,penalty="Asymptotic",pen.value=0.05,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" and "Manual" penalties. If Manual is specified, the manual penalty is contained in the pen.value parameter. The predefined penalties listed do NOT count the changepoint as a parameter, postfix a 1 e.

pen.value

The value of the penalty when using the Manual penalty option. This can be a numeric value or text giving the formula to use. Available variables are, n=length of original data, null=test statistic, tau=proposed changepoint, diffparam=difference in numb

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

Warning: The prescribed penalty values are not defined for use on CUSUM tests. The values tend to be too large and thus manual penalties are preferred.

References

M. Csorgo, L. Horvath (1997) Limit Theorems in Change-Point Analysis, Wiley

E. S. Page (1954) Continuous Inspection Schemes, Biometrika 41(1/2), 100--115

See Also

cpt.mean,cpt

Examples

# Example of a change in mean at 100 in simulated normal data
set.seed(1)
x=c(rnorm(100,0,1),rnorm(100,10,1))
single.mean.cusum(x,penalty="Manual",pen.value=1,class=FALSE) # returns 101 to show that the null
#hypothesis was rejected and the change in mean is at 101
ans=single.mean.cusum(x,penalty="Manual",pen.value=1) 
cpts(ans) # returns 101 to show that the null hypothesis was rejected, the change in mean is at 101


# Example of a data matrix containing 2 rows, row 1 has a change in mean and row 2 had no change in
#mean
set.seed(1)
x=c(rnorm(100,0,1),rnorm(100,10,1))
y=rnorm(200,0,1)
z=rbind(x,y)
single.mean.cusum(z,penalty="Manual",pen.value=1,class=FALSE) # returns vector c(101,200) which
#shows that the first dataset has a change in mean at 101 and the second dataset rejected H1 and has
#no change in mean
ans=single.mean.cusum(z,penalty="Manual",pen.value="log(log(n))") 
cpts(ans[[1]]) # test using a manual penalty which is the log(SIC) penalty and gives the same values
#for this example 
cpts(ans[[2]]) # result is the same as above, c(101, 200)