AIC: Computes the AIC/BIC measure for output from the envcpt...
In EnvCpt: Detection of Structural Changes in Climate and Environment Time Series
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
Uses the likelihood and number of parameters from the output of the envcpt function and calculates the AIC/BIC measure for each model.
Usage
1
2
3
4
Arguments
object
A list produced as output from the envcpt function. In essence any list where the first element contains a matrix whose first row is twice the negative log-likelihood and second row is the number of parameters. Columns are different models to compare.
...
Used to pass the length of the data to the BIC function as argument n.
k
numeric, the penalty per parameter to be used: the default k=2 is the classical AIC. The value log(n) is hard coded into BIC.
Details
Calculates the AIC defined as -2*<log-likelihood> + 2*<number of parameters> or the BIC as -2*<log-likelihood> + log(n)*<number of parameters>. When comparing models the smaller the AIC/BIC the better the fit.
Value
Vector of AIC/BIC values the same length as the number of columns in the first entry to the input list (length 12 if output from envcpt is used). The column names from the envcpt output are preserved to give clear indication on models.
Author(s)
Simon Taylor and Rebecca Killick
See Also
Examples
1
2
3
4
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7
8
9
10
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12
13
14
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18
19
20
21
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## Not run:
set.seed(1)
x=c(rnorm(100,0,1),rnorm(100,5,1))
out=envcpt(x) # run all models with default values
out[[1]] # first row is twice the negative log-likelihood for each model
# second row is the number of parameters
AIC(out) # returns AIC for each model.
which.min(AIC(out)) # gives meancpt (model 2) as the best model fit.
out$meancpt # gives the model fit for the meancpt model.
AICweights(out) # gives the AIC weights for each model
BIC(out) # returns the BIC for each model.
which.min(BIC(out)) # gives meancpt (model 2) as the best model fit too.
plot(out,type='fit') # plots the fits
plot(out,type="aic") # plots the aic values
plot(out,type="bic") # plots the bic values
set.seed(10)
x=c(0.01*(1:100),1.5-0.02*((101:250)-101))+rnorm(250,0,0.2)
out=envcpt(x,minseglen=10) # run all models with a minimum of 10 observations between changes
AIC(out) # returns the AIC for each model
which.min(AIC(out)) # gives trendcpt (model 8) as the best model fit.
out$trendcpt # gives the model fit for the trendcpt model.
AICweights(out) # gives the AIC weights for each model
BIC(out) # returns the BIC for each model.
which.min(BIC(out)) # gives trendcpt (model 8) as the best model fit too.
plot(out,type='fit') # plots the fits
plot(out,type="aic") # plots the aic values
plot(out,type="bic") # plots the bic values
set.seed(100)
x=arima.sim(model=list(ar=c(0.7,0.2)),n=500)+0.01*(1:500)
out=envcpt(x,models=c(3:6,9:12)) # runs a subset of models (those with AR components)
AIC(out) # returns the AIC for each model
which.min(AIC(out)) # gives trendar2 (model 10) as the best model fit.
out$trendar2 # gives the model fit for the trendar2 model. Notice that the trend is tiny but does
# produce a significantly better fit than the meanar2 model.
AICweights(out) # gives the AIC weights for each model
BIC(out) # returns the BIC for each model.
which.min(BIC(out)) # best fit is trendar2 (model 10) again.
plot(out,type='fit') # plots the fits
plot(out,type="aic") # plots the aic values
plot(out,type="bic") # plots the bic values
## End(Not run)
Example output
Loading required package: changepoint
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Successfully loaded changepoint package version 2.2.2
NOTE: Predefined penalty values changed in version 2.2. Previous penalty values with a postfix 1 i.e. SIC1 are now without i.e. SIC and previous penalties without a postfix i.e. SIC are now with a postfix 0 i.e. SIC0. See NEWS and help files for further details.
Loading required package: MASS
Fitting 12 models
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|========================================================== | 83%
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|================================================================ | 92%
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|======================================================================| 100%
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt trend
logLik 949.2517 535.486 683.8642 640.5247 532.9724 530.5236 735.4193
nparam 2.0000 5.000 3.0000 4.0000 7.0000 9.0000 3.0000
trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
logLik 535.414 648.192 619.5107 532.7957 530.4183
nparam 7.000 4.000 5.0000 9.0000 11.0000
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
953.2517 545.4860 689.8642 648.5247 546.9724 548.5236
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
741.4193 549.4140 656.1920 629.5107 550.7957 552.4183
meancpt
2
Class 'cpt' : Changepoint Object
~~ : S4 class containing 12 slots with names
cpttype date version data.set method test.stat pen.type pen.value minseglen cpts ncpts.max param.est
Created on : Thu May 4 11:08:19 2017
summary(.) :
----------
Created Using changepoint version 2.2.2
Changepoint type : Change in mean and variance
Method of analysis : PELT
Test Statistic : Normal
Type of penalty : MBIC with value, 21.19327
Minimum Segment Length : 5
Maximum no. of cpts : Inf
Changepoint Locations : 100
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
1.471637e-89 5.164235e-01 2.299732e-32 2.179893e-23 2.456047e-01 1.130823e-01
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
1.467638e-43 7.245090e-02 4.715216e-25 2.932684e-19 3.630777e-02 1.613078e-02
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
959.8483 561.9775 699.7591 661.7179 570.0606 578.2084
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
751.3143 572.5022 669.3852 646.0023 580.4806 588.6998
meancpt
2
Fitting 12 models
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|================================================================ | 92%
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mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
578.94707 -67.51376 27.29077 -29.55647 27.29077 29.29077
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
468.36581 -113.41437 20.92805 -33.70269 -109.94452 -105.29104
trendcpt
8
Class 'cpt.reg' : Changepoint Regression Object
~~ : S4 class containing 12 slots with names
cpttype date version data.set method test.stat pen.type pen.value minseglen cpts ncpts.max param.est
Created on : Thu May 4 11:08:19 2017
summary(.) :
----------
Created Using changepoint version 2.2.2
Changepoint type : Change in regression
Method of analysis : PELT
Test Statistic : Normal
Type of penalty : MBIC with value, 27.6073
Maximum no. of cpts : Inf
Changepoint Locations : 100
mean meancpt meanar1 meanar2 meanar1cpt
3.790989e-151 9.035235e-11 2.340974e-31 5.171508e-19 2.340974e-31
meanar2cpt trend trendcpt trendar1 trendar2
8.611961e-32 3.900936e-127 8.377773e-01 5.636952e-30 4.111095e-18
trendar1cpt trendar2cpt
1.477958e-01 1.442682e-02
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
585.98999 24.04422 37.85515 -15.47062 37.85515 43.37661
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
478.93019 -88.76414 35.01389 -16.09538 -78.25138 -66.55497
trendcpt
8
Fitting 8 models
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mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
NA NA 1478.915 1455.634 1478.915 1480.915
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
NA NA 1452.451 1430.101 1452.451 1430.101
trendar2
10
Call:
lm(formula = data[-c(1:2)] ~ c(1:(n - 2)) + data[2:(n - 1)] +
data[1:(n - 2)])
Coefficients:
(Intercept) c(1:(n - 2)) data[2:(n - 1)] data[1:(n - 2)]
-0.069419 0.001703 0.661337 0.186613
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
NA NA 1.256735e-11 1.428051e-06 1.256735e-11 4.623269e-12
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
NA NA 7.011284e-06 4.999923e-01 7.011284e-06 4.999923e-01
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
NA NA 1491.553 1472.484 1491.553 1497.765
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
NA NA 1469.302 1451.164 1469.302 1451.164
trendar2
10
EnvCpt documentation built on March 29, 2021, 5:11 p.m.
R Package Documentation
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Description Usage Arguments Details Value Author(s) See Also Examples
Description
Uses the likelihood and number of parameters from the output of the envcpt function and calculates the AIC/BIC measure for each model.
Usage
1 2 3 4 |
Arguments
object |
A list produced as output from the |
... |
Used to pass the length of the data to the BIC function as argument |
k |
numeric, the penalty per parameter to be used: the default |
Details
Calculates the AIC defined as -2*<log-likelihood> + 2*<number of parameters> or the BIC as -2*<log-likelihood> + log(n)*<number of parameters>. When comparing models the smaller the AIC/BIC the better the fit.
Value
Vector of AIC/BIC values the same length as the number of columns in the first entry to the input list (length 12 if output from envcpt is used). The column names from the envcpt output are preserved to give clear indication on models.
Author(s)
Simon Taylor and Rebecca Killick
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 | ## Not run:
set.seed(1)
x=c(rnorm(100,0,1),rnorm(100,5,1))
out=envcpt(x) # run all models with default values
out[[1]] # first row is twice the negative log-likelihood for each model
# second row is the number of parameters
AIC(out) # returns AIC for each model.
which.min(AIC(out)) # gives meancpt (model 2) as the best model fit.
out$meancpt # gives the model fit for the meancpt model.
AICweights(out) # gives the AIC weights for each model
BIC(out) # returns the BIC for each model.
which.min(BIC(out)) # gives meancpt (model 2) as the best model fit too.
plot(out,type='fit') # plots the fits
plot(out,type="aic") # plots the aic values
plot(out,type="bic") # plots the bic values
set.seed(10)
x=c(0.01*(1:100),1.5-0.02*((101:250)-101))+rnorm(250,0,0.2)
out=envcpt(x,minseglen=10) # run all models with a minimum of 10 observations between changes
AIC(out) # returns the AIC for each model
which.min(AIC(out)) # gives trendcpt (model 8) as the best model fit.
out$trendcpt # gives the model fit for the trendcpt model.
AICweights(out) # gives the AIC weights for each model
BIC(out) # returns the BIC for each model.
which.min(BIC(out)) # gives trendcpt (model 8) as the best model fit too.
plot(out,type='fit') # plots the fits
plot(out,type="aic") # plots the aic values
plot(out,type="bic") # plots the bic values
set.seed(100)
x=arima.sim(model=list(ar=c(0.7,0.2)),n=500)+0.01*(1:500)
out=envcpt(x,models=c(3:6,9:12)) # runs a subset of models (those with AR components)
AIC(out) # returns the AIC for each model
which.min(AIC(out)) # gives trendar2 (model 10) as the best model fit.
out$trendar2 # gives the model fit for the trendar2 model. Notice that the trend is tiny but does
# produce a significantly better fit than the meanar2 model.
AICweights(out) # gives the AIC weights for each model
BIC(out) # returns the BIC for each model.
which.min(BIC(out)) # best fit is trendar2 (model 10) again.
plot(out,type='fit') # plots the fits
plot(out,type="aic") # plots the aic values
plot(out,type="bic") # plots the bic values
## End(Not run)
|
Example output
Loading required package: changepoint
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Successfully loaded changepoint package version 2.2.2
NOTE: Predefined penalty values changed in version 2.2. Previous penalty values with a postfix 1 i.e. SIC1 are now without i.e. SIC and previous penalties without a postfix i.e. SIC are now with a postfix 0 i.e. SIC0. See NEWS and help files for further details.
Loading required package: MASS
Fitting 12 models
|
| | 0%
|
|====== | 8%
|
|============ | 17%
|
|================== | 25%
|
|======================= | 33%
|
|============================= | 42%
|
|=================================== | 50%
|
|========================================= | 58%
|
|=============================================== | 67%
|
|==================================================== | 75%
|
|========================================================== | 83%
|
|================================================================ | 92%
|
|======================================================================| 100%
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt trend
logLik 949.2517 535.486 683.8642 640.5247 532.9724 530.5236 735.4193
nparam 2.0000 5.000 3.0000 4.0000 7.0000 9.0000 3.0000
trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
logLik 535.414 648.192 619.5107 532.7957 530.4183
nparam 7.000 4.000 5.0000 9.0000 11.0000
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
953.2517 545.4860 689.8642 648.5247 546.9724 548.5236
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
741.4193 549.4140 656.1920 629.5107 550.7957 552.4183
meancpt
2
Class 'cpt' : Changepoint Object
~~ : S4 class containing 12 slots with names
cpttype date version data.set method test.stat pen.type pen.value minseglen cpts ncpts.max param.est
Created on : Thu May 4 11:08:19 2017
summary(.) :
----------
Created Using changepoint version 2.2.2
Changepoint type : Change in mean and variance
Method of analysis : PELT
Test Statistic : Normal
Type of penalty : MBIC with value, 21.19327
Minimum Segment Length : 5
Maximum no. of cpts : Inf
Changepoint Locations : 100
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
1.471637e-89 5.164235e-01 2.299732e-32 2.179893e-23 2.456047e-01 1.130823e-01
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
1.467638e-43 7.245090e-02 4.715216e-25 2.932684e-19 3.630777e-02 1.613078e-02
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
959.8483 561.9775 699.7591 661.7179 570.0606 578.2084
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
751.3143 572.5022 669.3852 646.0023 580.4806 588.6998
meancpt
2
Fitting 12 models
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|====== | 8%
|
|============ | 17%
|
|================== | 25%
|
|======================= | 33%
|
|============================= | 42%
|
|=================================== | 50%
|
|========================================= | 58%
|
|=============================================== | 67%
|
|==================================================== | 75%
|
|========================================================== | 83%
|
|================================================================ | 92%
|
|======================================================================| 100%
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
578.94707 -67.51376 27.29077 -29.55647 27.29077 29.29077
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
468.36581 -113.41437 20.92805 -33.70269 -109.94452 -105.29104
trendcpt
8
Class 'cpt.reg' : Changepoint Regression Object
~~ : S4 class containing 12 slots with names
cpttype date version data.set method test.stat pen.type pen.value minseglen cpts ncpts.max param.est
Created on : Thu May 4 11:08:19 2017
summary(.) :
----------
Created Using changepoint version 2.2.2
Changepoint type : Change in regression
Method of analysis : PELT
Test Statistic : Normal
Type of penalty : MBIC with value, 27.6073
Maximum no. of cpts : Inf
Changepoint Locations : 100
mean meancpt meanar1 meanar2 meanar1cpt
3.790989e-151 9.035235e-11 2.340974e-31 5.171508e-19 2.340974e-31
meanar2cpt trend trendcpt trendar1 trendar2
8.611961e-32 3.900936e-127 8.377773e-01 5.636952e-30 4.111095e-18
trendar1cpt trendar2cpt
1.477958e-01 1.442682e-02
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
585.98999 24.04422 37.85515 -15.47062 37.85515 43.37661
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
478.93019 -88.76414 35.01389 -16.09538 -78.25138 -66.55497
trendcpt
8
Fitting 8 models
|
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|
|========================== | 38%
|
|=================================== | 50%
|
|============================================ | 62%
|
|==================================================== | 75%
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
NA NA 1478.915 1455.634 1478.915 1480.915
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
NA NA 1452.451 1430.101 1452.451 1430.101
trendar2
10
Call:
lm(formula = data[-c(1:2)] ~ c(1:(n - 2)) + data[2:(n - 1)] +
data[1:(n - 2)])
Coefficients:
(Intercept) c(1:(n - 2)) data[2:(n - 1)] data[1:(n - 2)]
-0.069419 0.001703 0.661337 0.186613
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
NA NA 1.256735e-11 1.428051e-06 1.256735e-11 4.623269e-12
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
NA NA 7.011284e-06 4.999923e-01 7.011284e-06 4.999923e-01
mean meancpt meanar1 meanar2 meanar1cpt meanar2cpt
NA NA 1491.553 1472.484 1491.553 1497.765
trend trendcpt trendar1 trendar2 trendar1cpt trendar2cpt
NA NA 1469.302 1451.164 1469.302 1451.164
trendar2
10
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