EGARCH Error Distribution Simulation

This project runs a Monte Carlo simulation study for EGARCH(1,1) models under several innovation distributions and compares model recovery across sample sizes.

The detailed simulation methodology is documented in docs/simulation-procedure.md. Cluster batch instructions are documented in docs/cluster-batch.md.

Project Structure

.
├── R/
│   ├── simulation_config.R      # Monte Carlo design and true parameters
│   ├── simulation_functions.R   # EGARCH simulation and model fitting
│   ├── simulation_summaries.R   # AIC/BIC selection and recovery metrics
│   ├── simulation_plots.R       # Plot and output helpers
│   ├── simulations.R            # Main local runner
│   ├── batch_run.R              # One cluster batch chunk
│   └── combine_batch_results.R  # Combine batch chunks
├── data/                        # Optional local inputs, if added later
├── docs/                        # Project documentation and methodology notes
├── scripts/                     # SLURM and batch helper scripts
│   └── make-paper-latex-tables.R # Convert paper-style CSV tables to LaTeX
├── results/                     # Generated tables, plots, and saved outputs
├── README.md
└── renv.lock                    # Reproducible R package environment

Requirements

• R 4.4.0 or later
• renv

The main analysis uses:

• rugarch
• dplyr
• tidyr
• purrr
• ggplot2

Setup

Restore the R environment with:

renv::restore()

If renv is not installed yet:

install.packages("renv")
renv::restore()

Run the Simulation

From the project root:

source("R/simulations.R")

The default design follows docs/simulation-procedure.md: 5000 replications, sample sizes 50, 500, 1000, and 2000, five true innovation distributions, and five fitted candidate distributions for each simulated series. This is a large run.

For cluster execution, use the batch workflow in docs/cluster-batch.md.

Quick Test Run

Use environment variables to run a smaller version without editing the code:

EGARCH_REPS=1 EGARCH_SAMPLE_SIZES=50 EGARCH_OUTPUT_DIR=results/smoke-test Rscript R/simulations.R

You can also load the functions without running the full simulation:

options(egarch.run_on_source = FALSE)
source("R/simulations.R")

Outputs

Simulation outputs are written to results/ by default:

• sim_results.csv
• fit_summary.csv
• aic_selection_frequency.csv
• bic_selection_frequency.csv
• parameter_summary.csv
• simulation_outputs.rds
• plot PNG and PDF files, including aic_selection, bic_selection, convergence_rate, information_criteria, parameter_rmse, parameter_rmse_heatmap*, rmse_distribution, volatility_rmse, and volatility_rmse_large_n

Paper-style summary tables are written to results/paper_tables/, with LaTeX exports and a combined preview bundle in results/paper_tables/latex/.

To regenerate the LaTeX tables from the CSV inputs, run:

source("scripts/make-paper-latex-tables.R")

Notes

• Generated outputs should be saved under results/.
• Large intermediate files, local data, and rendered output are ignored by Git by default.
• rugarch uses a positive skew parameter where 1 is symmetry. The documented skew value of -0.5 is implemented as 0.5, representing moderate left-skewness in rugarch.