Log Likelihood and Information Criteria for Breakpoints

Description

Computation of log likelihood and AIC type information criteria for partitions given by breakpoints.

Usage

## S3 method for class 'breakpointsfull'
logLik(object, breaks = NULL, ...)
## S3 method for class 'breakpointsfull'
AIC(object, breaks = NULL, ..., k = 2)

Arguments

object	an object of class “breakpoints” or “breakpointsfull”.
breaks	if object is of class “breakpointsfull” the number of breaks can be specified.
…	currently not used.
k	the penalty parameter to be used, the default k = 2 is the classical AIC, k = log(n) gives the BIC, if n is the number of observations.

Details

As for linear models the log likelihood is computed on a normal model and the degrees of freedom are the number of regression coefficients multiplied by the number of segments plus the number of estimated breakpoints plus 1 for the error variance.

If AIC is applied to an object of class “breakpointsfull” breaks can be a vector of integers and the AIC for each corresponding partition will be returned. By default the maximal number of breaks stored in the object is used. See below for an example.

Value

An object of class “logLik” or a simple vector containing the AIC respectively.

See Also

breakpoints

Examples

library("strucchange")

## Nile data with one breakpoint: the annual flows drop in 1898
## because the first Ashwan dam was built
data("Nile")
plot(Nile)

bp.nile <- breakpoints(Nile ~ 1)
summary(bp.nile)

     Optimal (m+1)-segment partition: 

Call:
breakpoints.formula(formula = Nile ~ 1)

Breakpoints at observation number:
                      
m = 1      28         
m = 2      28       83
m = 3      28    68 83
m = 4      28 45 68 83
m = 5   15 30 45 68 83

Corresponding to breakdates:
                                
m = 1        1898               
m = 2        1898           1953
m = 3        1898      1938 1953
m = 4        1898 1915 1938 1953
m = 5   1885 1900 1915 1938 1953

Fit:
                                                   
m   0       1       2       3       4       5      
RSS 2835157 1597457 1552924 1538097 1507888 1659994
BIC    1318    1270    1276    1285    1292    1311

plot(bp.nile)

## BIC of partitions with0 to 5 breakpoints
plot(0:5, AIC(bp.nile, k = log(bp.nile$nobs)), type = "b")

## AIC
plot(0:5, AIC(bp.nile), type = "b")

## BIC, AIC, log likelihood of a single partition
bp.nile1 <- breakpoints(bp.nile, breaks = 1)
AIC(bp.nile1, k = log(bp.nile1$nobs))

[1] 1270.084

AIC(bp.nile1)

[1] 1259.663

logLik(bp.nile1)

'log Lik.' -625.8315 (df=4)