Generating Synthetic Data with R-vine Copulas using esgtoolkit in R
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R-vine copulas are powerful tools for modeling complex dependencies among multiple variables. The esgtoolkit package in R provides a user-friendly interface to fit R-vine copula models and generate synthetic data that preserves the statistical properties of the original dataset.
See also:
- https://docs.techtonique.net/ESGtoolkit/index.html
- https://docs.techtonique.net/ESGtoolkit/articles/syntheticopula.html
devtools::install_github("Techtonique/esgtoolkit")
library(esgtoolkit)
y <- esgtoolkit::calculatereturns(ts(EuStockMarkets[1:250, ], start=start(EuStockMarkets),
frequency=frequency(EuStockMarkets)), type = "log")
# Run simulation
result <- simulate_rvine(y, n = 500, verbose = TRUE, n_trials = 5)
# Print summary
print(result)
# Create different types of plots
plot(result, type = "distribution") # Default
plot(result, type = "correlation")
#plot(result, type = "both")
# Access detailed diagnostics
str(result$diagnostics)
# Access simulated data
sim_data <- result$simulated_data
head(sim_data)
Transforming data to uniform margins with improved boundary handling...
Fitting R-vine copula model...
V1 + V3 --> V1,V3 ; V2
V2 + V4 --> V2,V4 ; V3
V1 + V4 --> V1,V4 ; V3,V2
R-vine copula model fitted successfully
tree edge | family cop par par2 | tau utd ltd
-----------------------------------------------------------
1 2,1 | 19 SBB7 2.03 0.69 | 0.47 0.36 0.59
3,2 | 19 SBB7 1.74 0.79 | 0.44 0.41 0.51
4,3 | 1 N 0.63 0.00 | 0.43 - -
2 3,1;2 | 1 N 0.33 0.00 | 0.21 - -
4,2;3 | 1 N 0.30 0.00 | 0.19 - -
3 4,1;3,2 | 14 SG 1.07 0.00 | 0.06 - 0.09
---
type: D-vine logLik: 249.86 AIC: -483.71 BIC: -455.57
---
1 <-> V1, 2 <-> V2, 3 <-> V3, 4 <-> V4 tree edge family cop par par2 tau utd ltd
1 1 4,3 1 N 0.6297866 0.0000000 0.43371534 0.0000000 0.00000000
2 1 3,2 19 SBB7 1.7362736 0.7864981 0.43642959 0.4142407 0.50934532
3 1 2,1 19 SBB7 2.0325295 0.6856104 0.46867955 0.3638576 0.59360896
4 2 4,2;3 1 N 0.2984383 0.0000000 0.19293140 0.0000000 0.00000000
5 2 3,1;2 1 N 0.3282026 0.0000000 0.21288575 0.0000000 0.00000000
6 3 4,1;3,2 14 SG 1.0683573 0.0000000 0.06398351 0.0000000 0.08676182
Running 5 simulation trials...
Best simulation achieved quality score: 0.0984
Score weights used: [0.4, 0.2, 0.2, 0.1, 0.1]
Mean absolute correlation error (Kendall): 0.0077
Mean absolute correlation error (Pearson): 0.0428
R-vine Copula Simulation Results
================================
Original observations: 249
Variables: 4
Simulated observations: 500
Quality score: 0.0984
Successful trials: 5/5
Mean absolute correlation error (Kendall): 0.0077
Mean absolute correlation error (Pearson): 0.0428
Use plot() to visualize results and $diagnostics for detailed metrics.
List of 24
$ original_correlation_tau : num [1:4, 1:4] 1 0.465 0.413 0.353 0.465 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ simulated_correlation_tau : num [1:4, 1:4] 1 0.45 0.421 0.355 0.45 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ correlation_error_tau : num [1:4, 1:4] 0 -0.01499 0.00825 0.00173 -0.01499 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ original_correlation_pearson : num [1:4, 1:4] 1 0.815 0.728 0.507 0.815 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ simulated_correlation_pearson: num [1:4, 1:4] 1 0.766 0.682 0.404 0.766 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ correlation_error_pearson : num [1:4, 1:4] 0 -0.0483 -0.0454 -0.1027 -0.0483 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
.. ..$ : chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ mean_absolute_error_tau : num 0.0077
$ max_absolute_error_tau : num 0.0232
$ mean_absolute_error_pearson : num 0.0428
$ max_absolute_error_pearson : num 0.103
$ quality_score : num 0.0984
$ score_weights_used : num [1:5] 0.4 0.2 0.2 0.1 0.1
$ trial_scores : num [1:5] 0.219 0.1222 0.0984 0.1231 0.1884
$ successful_trials : int 5
$ RVM_model :List of 20
..$ Matrix : num [1:4, 1:4] 1 4 3 2 0 2 4 3 0 0 ...
..$ family : num [1:4, 1:4] 0 14 1 19 0 0 1 19 0 0 ...
..$ par : num [1:4, 1:4] 0 1.068 0.328 2.033 0 ...
..$ par2 : num [1:4, 1:4] 0 0 0 0.686 0 ...
..$ names : chr [1:4] "V1" "V2" "V3" "V4"
..$ MaxMat : num [1:4, 1:4] 1 2 2 2 0 2 3 3 0 0 ...
..$ CondDistr :List of 2
.. ..$ direct : logi [1:4, 1:4] FALSE TRUE TRUE TRUE FALSE FALSE ...
.. ..$ indirect: logi [1:4, 1:4] FALSE FALSE FALSE FALSE FALSE TRUE ...
..$ type : chr "D-vine"
..$ tau : num [1:4, 1:4] 0 0.064 0.213 0.469 0 ...
..$ taildep :List of 2
.. ..$ upper: num [1:4, 1:4] 0 0 0 0.364 0 ...
.. ..$ lower: num [1:4, 1:4] 0 0.0868 0 0.5936 0 ...
..$ beta : num [1:4, 1:4] 0 0.062 0.213 0.443 0 ...
..$ call : language VineCopula::RVineStructureSelect(data = U, familyset = valid_families, type = 0, selectioncrit = "BIC", trun| __truncated__ ...
..$ nobs : int 249
..$ logLik : num 250
..$ pair.logLik: num [1:4, 1:4] 0 2.59 14.33 84.82 0 ...
..$ AIC : num -484
..$ pair.AIC : num [1:4, 1:4] 0 -3.18 -26.66 -165.65 0 ...
..$ BIC : num -456
..$ pair.BIC : num [1:4, 1:4] 0 0.341 -23.138 -158.615 0 ...
..$ emptau : num [1:4, 1:4] 0 0.0639 0.2156 0.4653 0 ...
..- attr(*, "class")= chr "RVineMatrix"
$ n_observations : int 249
$ n_variables : int 4
$ n_simulations : num 500
$ original_means : Named num [1:4] 0.000372 0.000456 0.000338 0.000255
..- attr(*, "names")= chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ simulated_means : Named num [1:4] -3.17e-05 2.18e-04 -4.52e-05 1.83e-04
..- attr(*, "names")= chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ original_sds : Named num [1:4] 0.00931 0.00877 0.01049 0.00815
..- attr(*, "names")= chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ simulated_sds : Named num [1:4] 0.00954 0.00886 0.01119 0.00849
..- attr(*, "names")= chr [1:4] "DAX" "SMI" "CAC" "FTSE"
$ ks_test_statistics : Named num [1:4] 0.0259 0.0354 0.0507 0.04
..- attr(*, "names")= chr [1:4] "D" "D" "D" "D"
$ ks_test_pvalues : num [1:4] 1 0.985 0.786 0.953
| DAX | SMI | CAC | FTSE |
|---|---|---|---|
| -0.001398544 | -0.0015309795 | 0.003170410 | 0.0008758254 |
| 0.004458917 | 0.0026640098 | 0.011666435 | 0.0057322484 |
| -0.001597764 | -0.0001979084 | -0.004832143 | 0.0011097778 |
| -0.001501251 | -0.0034774275 | -0.003218613 | 0.0020315141 |
| 0.000000000 | 0.0045969506 | 0.001912011 | -0.0044810433 |
| -0.002419004 | -0.0004654500 | -0.004832588 | -0.0055430360 |
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