Dependence Analysis between Investment Funds and Macroeconomic Variables

About the Project

This repository contains the code used in the dissertation "Assessment of the dependency structure between Investment Funds and macroeconomic variables: An application of copula theory" developed at UERJ. The project analyzes the relationship between Brazilian investment funds and macroeconomic variables through three main approaches:

1. Cointegration Analysis (ARDL)
2. Causality Analysis (Toda-Yamamoto)
3. Copula Theory

Theoretical Background

This project combines three main theoretical approaches to analyze the relationship between investment funds and macroeconomic variables:

1. Copula Theory: Used to model complex dependency structures between variables, allowing for non-linear relationships and tail dependencies.

2. Cointegration Analysis: Employs ARDL bounds testing approach to investigate long-run relationships between variables that may be integrated of different orders.

3. Causality Testing: Utilizes the Toda-Yamamoto procedure to examine causal relationships while avoiding pre-test bias.

For detailed theoretical explanations and mathematical foundations, please refer to the documentation in the docs/ directory.

Project Structure

.
├── R/
│   ├── copula.R             # Functions for copula analysis
│   ├── cointegration.R      # Functions for ARDL cointegration tests
│   └── causality.R          # Functions for causality tests
├── data/
│   └── example_data/        # Example datasets
├── docs/
│   └── dissertation.pdf     # Full dissertation
├── tests/
│   └── testthat/           # Unit tests
├── LICENSE
└── README.md

Main Features

1. Copula Analysis (copula.R)

• Estimation of bivariate copulas
• Goodness-of-fit tests
• Data simulation
• Calculation of dependence measures
• Visualization of dependence structures

2. Cointegration Analysis (cointegration.R)

• Unit root tests (ADF)
• ARDL model estimation
• Bounds Testing
• Error correction analysis

3. Causality Analysis (causality.R)

• Implementation of Toda-Yamamoto test
• Modified Granger causality analysis
• Robustness tests

Requirements

# Required packages
install.packages(c(
  "tidyverse",
  "VineCopula",
  "fitdistrplus",
  "kdecopula",
  "urca",
  "vars",
  "collapse",
  "aod"
))

How to Use

Copula Analysis Example

source("R/copula.R")

# Load and prepare data
data <- read_data("path/to/data.csv")

# Find best distribution
dist_info <- find_best_distribution(data, distributions)

# Estimate copulas
copulas <- estimate_bivariate_copula(data, family)

# Simulate data
simulated_data <- simulate_bivariate_copula(copulas, orig_data, dist_info, 1000)

Cointegration Analysis Example

source("R/cointegration.R")

# ADF test
adf_results <- adf_test(data)

# ARDL estimation
ardl_model <- estimate_ardl(data_list, max_lag = 3)

# Bounds test
bound_test_results <- run_bound_test(ardl_model)

Documentation and Theoretical Background

The theoretical foundation of this project is documented in two main files in the docs/ directory:

1. dissertation.pdf - Contains detailed theoretical background on:

   • Copula theory and its applications
   • Different copula families
   • Estimation methods
   • Goodness-of-fit tests
   • Simulation procedures

2. impact_funds.pdf - Provides comprehensive information about:

   • ARDL cointegration methodology
   • Toda-Yamamoto causality testing
   • Application to investment funds
   • Empirical results and interpretation

These documents provide the theoretical framework and mathematical foundations for the implementations in this repository.

Technical Details

ARDL Cointegration Testing

The Autoregressive Distributed Lag (ARDL) approach to cointegration is used to test for long-run relationships between variables. This method has several advantages:

• Can be applied when variables are integrated of different orders
• Suitable for small sample sizes
• Allows for different lag lengths in the model

The bounds testing procedure involves:

1. Testing for unit roots to ensure no I(2) variables
2. Estimating the ARDL model
3. Computing the F-statistic for the bounds test
4. Testing for serial correlation, normality, and heteroscedasticity

Toda-Yamamoto Causality Testing

The Toda-Yamamoto approach to testing for Granger causality:

• Robust to different orders of integration
• Does not require pre-testing for cointegration
• Minimizes risks of pre-test bias

The procedure involves:

1. Determining the maximum order of integration (dmax)
2. Selecting the optimal lag length (k)
3. Estimating a VAR model in levels with k + dmax lags
4. Performing modified Wald tests

Contributing

Contributions are welcome! Please read CONTRIBUTING.md for details on our code of conduct and the process for submitting pull requests.

Citation

If you use this code in your research, please cite:

@mastersthesis{arruda2024assessment,
  title={Assessment of the dependency structure between Investment Funds and macroeconomic variables: An application of copula theory},
  author={Arruda, Gabriel de Almeida},
  school={Rio de Janeiro State University},
  year={2024}
}