Empirical Copula Fitting and Model Criteria

Code Stratmill research code

Summary

This module supports copula analysis by mapping observations to marginal empirical cumulative probabilities, with optional linear interpolation and probability bounds. It provides a multivariate row-wise transform, fits a supplied copula to two series after converting each through its empirical CDF, and returns the fitted model, the marginal transforms, log-likelihood-based information criteria, and model name. For Student-t copulas it also estimates the degrees of freedom within a bounded range. The module includes Schwarz, Akaike, and Hannan–Quinn criteria, plus SCAD penalty and derivative functions and a helper that drops small mixture weights and renormalizes the remainder.

These routines are useful building blocks for dependence modeling, including paired-series analysis, but the code itself does not establish a trading strategy or demonstrate out-of-sample performance. The empirical transforms are estimated from the supplied training observations, so practical use requires care to avoid look-ahead bias. The AIC implementation shown uses a finite-sample correction, and users should verify that its criterion definition matches their intended comparison. Copula fitting and Student-t degrees-of-freedom estimation also depend on data quality and optimization behavior.

Key ideas

Empirical marginal CDFs transform observed series into bounded quantile values before copula fitting.
Linear interpolation fills gaps between empirical CDF steps and supports values outside the training range.
The module fits copulas by maximum likelihood and reports information criteria for comparing fit.
Student-t copula fitting includes a bounded estimate of its degrees of freedom.
SCAD penalties and mixture-weight thresholding support sparse selection among copula components.

Preparing Empirical Data and Fitting Copulas with Information Criteria

Summary

Key ideas

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