What is Copula ? (About DeepVAR and GPVAR)

[ken-take-it-so-so]

Hello. I'm still learning Python and GluonTS.
I want to use "gluonts.model.deepvar.DeepVAREstimator" and "gluonts.model.gpvar.GPVAREstimator". According to GluonTS documentation, these models are introduced in this paper: High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes
However, I don't know what Copula is. A below figure is in the paper.

When I want to try "Vec-LSTM-lowrank-Copula", how should I set arguments in DeepVAREstimator ? Especially, could you teach me how to use "Copula" ?
Moreover, in gluonts.model.gpvar package, it seems that GPVAR implements "GP-Copula". Then, when I want to try "GP" and "GP-scaling", how should I set arguments in GPVAR ?

I would appreciate your cooperation.

[jgasthaus]

"Copula" here refers to whether the marginal distributions are transformed to be (approximately) Gaussian before the model is applied. This is controlled by the use_marginal_transformation parameter which can be set when constructing both GPVar and DeepVar estimators. Setting this parameter to True will give you the Copula variants. Scaling is enabled by setting scaling=True.

gluonts/src/gluonts/mx/model/gpvar/_estimator.py

Line 132 in 015ff06

use_marginal_transformation

[ken-take-it-so-so]

@jgasthaus, thank you for your response. Lastly, let me ask an additional question. Should I set scaling=False when I try "-Copula" model in the figure ?

[jgasthaus]

Yes. Additional scaling is not necessary when using the marginal transform.

[ken-take-it-so-so]

Thank you ! I enjoyed chatting with you !!