Comprehensive Collection of Debugged Copula Application Examples with MATLAB Source Code

This resource provides a comprehensive collection of successfully debugged Copula application examples along with complete MATLAB source code. The case study focuses on a bivariate Copula model and its validation for daily returns from the Shanghai and Shenzhen stock markets. Below we present detailed information about this specific case.

First, what Copula model is used in this case? Copula is a method for describing dependencies between random variables. The model decomposes joint distributions into two components: marginal distributions and a Copula function, thereby achieving more accurate dependency characterization. In this implementation, we employ a bivariate Copula model since we're analyzing the relationship between two variables. The MATLAB code includes functions for parameter estimation using maximum likelihood methods and implements various Copula families (Gaussian, t, Clayton, Gumbel) with proper boundary handling.

Second, how was the validation performed? To ensure result reliability, we implemented multiple validation methodologies. Initially, we conducted goodness-of-fit tests to evaluate the Copula model's fitting performance using probability integral transform and Cramér-von Mises statistics. Then, we applied Spearman's rank correlation coefficient and Kendall's rank correlation coefficient to validate the dependency structure captured by the Copula model. The code implements these correlation measures with efficient ranking algorithms and statistical significance testing. Finally, we employed Value-at-Risk (VaR) methodology for risk estimation, incorporating Monte Carlo simulation with variance reduction techniques for improved computational efficiency.

In summary, this case provides a complete Copula application example with comprehensive MATLAB source code. Beyond presenting the case itself, we include detailed explanations of Copula model fundamentals and validation methodologies, aiming to provide valuable insights for readers. The code architecture follows modular design principles with separate functions for data preprocessing, parameter estimation, model validation, and risk calculation, ensuring maintainability and extensibility.