envcpt: Assesses whether an environmental time series contains trend,...
In EnvCpt: Detection of Structural Changes in Climate and Environment Time Series
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Evaluates up to 12 different models (see details) and returns the model fits as well as a summary of the likelihood for each model.
Usage
1
2
3
Arguments
data
A vector or ts object containing the data to fit the models to.
models
A vector containing the subset of models to fit, defaults to all available models. This can either be named (as in the default) or numbered (1:12), see details or defaults for number-model pairings.
minseglen
Positive integer giving the minimum segment length (no. of observations between changes) for the changepoint models, default is the minimum allowed by theory (for the largest model).
...
Additional arguments to pass to the changepoint functions, if none are specified defaults with PELT multiple changepoint algorithm are used. See cpt.meanvar for options.
verbose
If TRUE (default), prints to the console an progress bar indicating progression through the fit of the up to 12 models.
Details
This function is used to automatically fit up to 12 different models all with Normal distribution for errors:
1. A constant mean and variance (using fitdistr)
2. A piecewise constant mean and variance (using cpt.meanvar)
3. A constant mean with AR (1) errors (using arima)
4. A constant mean with AR (2) errors (using arima)
5. A piecewise constant mean with AR(1) errors (using cpt.reg in this package - not exported)
6. A piecewise constant mean with AR(2) errors (using cpt.reg in this package - not exported)
7. A linear trend over time (using lm)
8. A piecewise linear trend over time (using cpt.reg in this package - not exported)
9. A linear trend over time with AR(1) errors (using lm)
10. A linear trend over time with AR(2) errors (using lm)
11. A piecewise linear trend over time with AR(1) errors (using cpt.reg in this package - not exported)
12. A piecewise linear trend over time with AR(2) errors (using cpt.reg in this package - not exported)
The default values for each function are used, except for the changepoint functions where multiple changes are identified and thus the PELT algorithm is used (see references or changepoint package for details).
Value
envcpt outputs a list of 13 elements. The first element is a 2x8 matrix where the first row contains the likelihood for each model fit and the second row contains the number of parameters fit in each model. The 12 columns are for the 12 different models in the order above (headings given). If any element is NA then either there was an error fitting this type of model (typically the AR models and this implies nonstationarity) or the model was not specified in the models argument.
Elements 2-13 of the list are the fits for each individual model, these are the direct output from the respective functions so see the individual functions for formats. The first model fit is in element 2 and the twelth model fit is in element 13, but are named for convenience.
Author(s)
Rebecca Killick
References
EnvCpt Algorithm: Beaulieu, C, Killick, R (2018+) Distinguishing trends and shifts from memory in climate data.
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
See Also
cpt.meanvar,plot-methods,cpt, plot.envcpt
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
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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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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) References See Also Examples
Description
Evaluates up to 12 different models (see details) and returns the model fits as well as a summary of the likelihood for each model.
Usage
1 2 3 |
Arguments
data |
A vector or ts object containing the data to fit the models to. |
models |
A vector containing the subset of models to fit, defaults to all available models. This can either be named (as in the default) or numbered (1:12), see details or defaults for number-model pairings. |
minseglen |
Positive integer giving the minimum segment length (no. of observations between changes) for the changepoint models, default is the minimum allowed by theory (for the largest model). |
... |
Additional arguments to pass to the changepoint functions, if none are specified defaults with PELT multiple changepoint algorithm are used. See |
verbose |
If TRUE (default), prints to the console an progress bar indicating progression through the fit of the up to 12 models. |
Details
This function is used to automatically fit up to 12 different models all with Normal distribution for errors:
1. A constant mean and variance (using fitdistr)
2. A piecewise constant mean and variance (using cpt.meanvar)
3. A constant mean with AR (1) errors (using arima)
4. A constant mean with AR (2) errors (using arima)
5. A piecewise constant mean with AR(1) errors (using cpt.reg in this package - not exported)
6. A piecewise constant mean with AR(2) errors (using cpt.reg in this package - not exported)
7. A linear trend over time (using lm)
8. A piecewise linear trend over time (using cpt.reg in this package - not exported)
9. A linear trend over time with AR(1) errors (using lm)
10. A linear trend over time with AR(2) errors (using lm)
11. A piecewise linear trend over time with AR(1) errors (using cpt.reg in this package - not exported)
12. A piecewise linear trend over time with AR(2) errors (using cpt.reg in this package - not exported)
The default values for each function are used, except for the changepoint functions where multiple changes are identified and thus the PELT algorithm is used (see references or changepoint package for details).
Value
envcpt outputs a list of 13 elements. The first element is a 2x8 matrix where the first row contains the likelihood for each model fit and the second row contains the number of parameters fit in each model. The 12 columns are for the 12 different models in the order above (headings given). If any element is NA then either there was an error fitting this type of model (typically the AR models and this implies nonstationarity) or the model was not specified in the models argument.
Elements 2-13 of the list are the fits for each individual model, these are the direct output from the respective functions so see the individual functions for formats. The first model fit is in element 2 and the twelth model fit is in element 13, but are named for convenience.
Author(s)
Rebecca Killick
References
EnvCpt Algorithm: Beaulieu, C, Killick, R (2018+) Distinguishing trends and shifts from memory in climate data.
PELT Algorithm: Killick R, Fearnhead P, Eckley IA (2012) Optimal detection of changepoints with a linear computational cost, JASA 107(500), 1590–1598
MBIC: Zhang, N. R. and Siegmund, D. O. (2007) A Modified Bayes Information Criterion with Applications to the Analysis of Comparative Genomic Hybridization Data. Biometrics 63, 22-32.
See Also
cpt.meanvar,plot-methods,cpt, plot.envcpt
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
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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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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
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