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Choosing a Model

Choose the dependence structure first, then decide whether it needs to vary over time. Fit a constant MLE baseline before adding GAS or latent SCAR dynamics so that the dynamic model can be compared against a simpler nested question.

Model Selection

Goal Suggested model Start with
Dependence between two variables GumbelCopula, ClaytonCopula, FrankCopula, JoeCopula, or BivariateGaussianCopula MLE
Time-varying dependence between two variables The same bivariate families GAS or SCAR-TM
Static Gaussian/Student dependence with supplied, plug-in, shrinkage, full, or factor correlation GaussianCopula or StudentCopula MLE plus an explicit corr_mode when the default fixed policy is not desired
One common correlation that changes over time EquicorrGaussianCopula GAS or SCAR-TM-OU
Time-varying multivariate tail thickness StochasticStudentCopula GAS or SCAR-TM-OU
Different pairwise families and dependence strengths VineCopula Auto R-vine or fixed C/D structure; MLE, then dynamic edges if needed
Very large dimension with low-rank correlation Gaussian or stochastic Student model with corr_mode="factor" Two-stage factor MLE

Use the Bivariate Copulas guide for one pair. For three or more variables, compare the assumptions in Multivariate Models, Factor Models, and Vine Copulas.

Estimation Choice

  • MLE uses one constant copula parameter and is the simplest baseline.
  • GAS makes dependence observation-driven and avoids latent-state integration.
  • SCAR-TM-OU models an unobserved mean-reverting state.
  • SCAR-TM-JACOBI models positive Kendall dependence directly on (0, 1).

See Estimation Methods for supported model-method combinations and fitting examples.

Prediction Choice

Use sample to reproduce a fitted model and predict to condition on the fitted history. Pass given={column: value} for conditional generation in pseudo-observation space.

The distinction between sampling, forecasting, and conditioning is covered in Prediction Semantics. For arbitrary R-vine conditioning sets, continue with R-vine Conditioning.

  1. Select a model family using the table above.
  2. Run the Quick Start.
  3. Fit an MLE baseline and inspect goodness of fit.
  4. Add GAS or SCAR only when time variation is part of the modeling question.
  5. Read Performance Tuning after the statistical model and estimation method are settled.