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

Crash Course: Copulas – Theory & Hands-On Project With R
Published 3/2025
MP4 | Video: h264, 1920×1080 | Audio: AAC, 44.1 KHz

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.

Curiosity and motivation to learn copula theory and its applications.

Description

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 7 Sklar’s Theorem

Lecture 10 Gaussian Copula: Scatter Plots

Lecture 13 t-Copula: Scatter Plots

Lecture 16 Clayton Copula: Scatter Plots

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

Lecture 26 Copula R Project

Lecture 27 R packages

Lecture 28 Data Import

Lecture 29 Data Visualization

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