changepoint (version 1.1.5)

cpt.mean: Identifying Changes in Mean

Description

Calculates the optimal positioning and (potentially) number of changepoints for data using the user specified method.

Usage

cpt.mean(data,penalty="SIC",pen.value=0,method="AMOC",Q=5,test.stat="Normal",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. 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, n

method

Choice of "AMOC", "PELT", "SegNeigh" or "BinSeg".

Q

The maximum number of changepoints to search for using the "BinSeg" method. The maximum number of segments (number of changepoints + 1) to search for using the "SegNeigh" method.

test.stat

The assumed test statistic / distribution of the data. Currently only "Normal" and "CUSUM" supported.

class

Logical. If TRUE then an object of class cpt 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 returned. For class=FALSE the structure is as follows.

  If data is a vector (single dataset) then a vector/list is returned depending on the value of method. If data is a matrix (multiple datasets) then a list is returned where each element in the list is either a vector or list depending on the value of method.

  If method is AMOC then a vector (one dataset) or matrix (multiple datasets) is returned, the columns are:

• cpt
  The most probable location of a changepoint if a change was identified or NA if no changepoint.
• p value
  The p-value of the identified changepoint.
• If method is PELT then a vector is returned containing the changepoint locations for the penalty supplied. This always ends with n. If method is SegNeigh then a list is returned with elements:
• cps
  Matrix containing the changepoint positions for 1,...,Q changepoints.
• op.cpts
  The optimal changepoint locations for the penalty supplied.
• pen
  Penalty used to find the optimal number of changepoints.
• like
  Value of the -2*log(likelihood ratio) + penalty for the optimal number of changepoints selected.
• If method is BinSeg then a list is returned with elements:
• cps
  2xQ Matrix containing the changepoint positions on the first row and the test statistic on the second row.
• op.cpts
  The optimal changepoint locations for the penalty supplied.
• pen
  Penalty used to find the optimal number of changepoints.

Details

This function is used to find changes in mean for data using the test statistic specfified in the test.stat parameter. The changes are found using the method supplied which can be single changepoint (AMOC) or multiple changepoints using exact (PELT or SegNeigh) or approximate (BinSeg) methods. A changepoint is denoted as the first observation of the new segment / regime.

References

Change in Normal mean: Hinkley, D. V. (1970) Inference About the Change-Point in a Sequence of Random Variables, Biometrika 57, 1--17

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

PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590--1598

Binary Segmentation: Scott, A. J. and Knott, M. (1974) A Cluster Analysis Method for Grouping Means in the Analysis of Variance, Biometrics 30(3), 507--512

Segment Neighbourhoods: Auger, I. E. And Lawrence, C. E. (1989) Algorithms for the Optimal Identification of Segment Neighborhoods, Bulletin of Mathematical Biology 51(1), 39--54

See Also

cpt.var,cpt.meanvar,plot-methods,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))
cpt.mean(x,penalty="SIC",method="AMOC",class=FALSE) # returns 100 to show that the null hypothesis
#was rejected and the change in mean is at 100
ans=cpt.mean(x,penalty="Asymptotic",pen.value=0.01,method="AMOC") 
cpts(ans)# returns 100 to show that the null hypothesis was rejected, the change in mean is at 100
#and we are 99% confident of this result
ans=cpt.mean(x,penalty="Manual",pen.value=0.8,method="AMOC",test.stat="CUSUM") # returns 101 as the
#changepoint location

# Example of multiple changes in mean at 50,100,150 in simulated normal data
set.seed(1)
x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1))
cpt.mean(x,penalty="Manual",pen.value="2*log(n)",method="BinSeg",Q=5,class=FALSE) # returns optimal
#number of changepoints is 3, locations are 50,100,150.

# Example multiple datasets where the first row has multiple changes in mean and the second row has
#no change in mean
set.seed(1)
x=c(rnorm(50,0,1),rnorm(50,5,1),rnorm(50,10,1),rnorm(50,3,1))
y=rnorm(200,0,1)
z=rbind(x,y)
cpt.mean(z,penalty="Asymptotic",pen.value=0.01,method="SegNeigh",Q=5,class=FALSE) # returns list
#that has two elements, the first has 3 changes in mean and variance at 50,100,150 and the second
#has no changes in variance
ans=cpt.mean(z,penalty="Asymptotic",pen.value=0.01,method="PELT") 
cpts(ans[[1]]) # same results as for the SegNeigh method.
cpts(ans[[2]]) # same results as for the SegNeigh method.