Crash Course: Copulas – Theory & Hands-On Project With R

Master Copula Theory, Visualization, Estimation, Simulation, and Probability Calculations with the copula Package in R

What you'll learn

Understand the fundamentals of copulas – Learn what copulas are, their mathematical properties, and their role in modeling dependence structures

Explore Sklar’s Theorem – Understand how joint cumulative distribution functions (CDFs) decompose into marginal distributions and a copula function

Learn different types of copulas – Study Gaussian, t-Student, Clayton, and Gumbel copulas, their characteristics, and how they capture different dependence stru

Estimate copula parameters in R – Use the copula package to estimate copula parameters through statistical methods

Perform goodness-of-fit tests – Assess the quality of fitted copula models using statistical criteria such as AIC, BIC, and log-likelihood

Visualize copulas in R – Generate contour plots, 3D surfaces, and scatter plots to interpret dependence structures

Simulate data using copulas – Use copulas to generate synthetic datasets that preserve the dependence structure of modeled data

Analyze dependencies – Compute Kendall’s Tau, Spearman’s Rho, and tail dependence coefficients to measure both typical and extreme event correlations

Requirements

Basic understanding of probability and statistics – Familiarity with concepts such as probability density functions (PDFs), cumulative distribution functions (CDFs), joint, marginal, and conditional distributions, as well as correlation.

Basic knowledge of statistical modeling and data analysis.

Familiarity with mathematical functions and their characteristics.

Willingness to work with mathematical formulas and apply them in R.

Ability to install and use R and RStudio on a computer.

Access to a computer with an internet connection to download necessary packages.

Introductory experience with R programming – Including data import, working with basic functions, and handling variables.

Curiosity and motivation to learn copula theory and its applications.

Patience and persistence to analyze dependencies between variables and apply copula-based techniques.

Description

"Crash Course: Copulas – Theory & Hands-On Project with R” is designed to introduce you to copula theory and its applications in statistical modeling using R. This course provides a structured approach to understanding copulas, from fundamental concepts to hands-on implementation with toy data.Who Is This Course For?No prior knowledge of copulas? No problem! This course is ideal for: Data scientists, statisticians, and analysts looking to model dependencies between variables. Finance, actuarial science, and risk management professionals interested in advanced dependence structures.Researchers and students seeking practical applications of copula models in various fields.R users looking to expand their skills with copula-based statistical modeling.What Does the Course Include?This course provides a comprehensive mix of theory and practice, ensuring a deep understanding of copulas and their real-world applications. You will: Learn the mathematical foundations of copulas, including Sklar’s Theorem. Explore different types of copulas – Gaussian, t-Student, Clayton, and Gumbel. Estimate copula parameters using the copula package in R. Perform goodness-of-fit tests to evaluate copula models. Visualize copula structures using scatter plots, contour plots, and 3D surfaces.Simulate and analyze dependencies using copula-based models. Compute marginal, joint, and conditional probabilities using copulas.Additional Learning ResourcesTo enhance your learning experience, this course includes practical coding exercises and step-by-step R implementations to reinforce key concepts.Why Take This Course?By the end of this course, you will be able to: Model and analyze dependencies between variables using copulas. Use R efficiently to implement copula-based statistical modeling. Apply copula models in finance, risk management, insurance, and data science.Ready to Get Started?Dive into the world of copulas and discover how they can revolutionize dependence modeling in statistics and data science.

Overview

Section 1: Introduction

Lecture 1 Introductory Notes

Section 2: Course Resources

Lecture 2 Course Resources

Section 3: A Brief Guide to Four Fundamental Copulas

Lecture 3 An Introduction to Copulas

Lecture 4 Copulas Adressed: Basic Characteristics

Lecture 5 d-Dimensional Copula Function

Lecture 6 Interactive 3D Plot Demonstrating Basic Properties of a Bivariate Copula

Lecture 7 Sklar's Theorem

Lecture 8 Elliptical Copulas: Multivariate Gaussian Copula

Lecture 9 Elliptical Copulas: Bivariate Gaussian Copula

Lecture 10 Gaussian Copula: Scatter Plots

Lecture 11 Elliptical Copulas: Multivariate t-Student Copula (t-Copula)

Lecture 12 Elliptical Copulas: Bivariate t-Student Copula (t-Copula)

Lecture 13 t-Copula: Scatter Plots

Lecture 14 Archimedean Copulas: Multivariate Clayton Copula

Lecture 15 Archimedean Copulas: Bivariate Clayton Copula

Lecture 16 Clayton Copula: Scatter Plots

Lecture 17 Archimedean Copulas: Multivariate Gumbel Copula

Lecture 18 Archimedean Copulas: Bivariate Gumbel Copula

Lecture 19 Gumbel Copula: Scatter Plots

Lecture 20 Tail Dependence

Lecture 21 Correlation

Lecture 22 Interactive Scatter Plots for Copulas: Gaussian, t, Clayton, and Gumbel

Lecture 23 t-Copula: Spearman’s Rho vs t-Copula Parameter

Lecture 24 Clayton Copula: Spearman’s Rho vs Clayton Copula Parameter

Lecture 25 Gumbel Copula: Spearman’s Rho vs Gumbel Copula Parameter

Section 4: Study of Two-Dimensional Distributions of Random Variable Using R copula package

Lecture 26 Copula R Project

Lecture 27 R packages

Lecture 28 Data Import

Lecture 29 Data Visualization

Lecture 30 Independence Test of Random Variables

Lecture 31 Data Transformation

Lecture 32 Copula Parameter Estimation

Lecture 33 Analysis of Estimated Parameters

Lecture 34 Verification of Fit Quality of Parameters

Lecture 35 Selection of the Best Copula

Lecture 36 Visual Analysis of the Copula

Lecture 37 Analysis of Correlation Dependencies

Lecture 38 Data Simulation

Lecture 39 Probability Calculations

Undergraduate and graduate students in statistics, mathematics, finance, economics, actuarial science, or related fields who want to understand dependence structures using copulas.,Data analysts, statisticians, and researchers interested in modeling and analyzing relationships between random variables beyond traditional correlation methods.,Finance and risk management professionals who need to model financial dependencies, portfolio risks, and credit scoring using copulas.,Actuaries and insurance analysts looking to apply copula models for risk aggregation and loss modeling.,Self-learners and R users eager to expand their knowledge of advanced statistical modeling techniques and hands-on R implementations.