OxiDiviner GARCH

A Rust implementation of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models for time series analysis and volatility forecasting.

Overview

GARCH models are widely used for analyzing and forecasting volatility in financial time series data. This crate provides a robust implementation of GARCH(p,q) models, suitable for financial analysis, risk management, and econometric modeling.

Features

• Full implementation of GARCH(p,q) models
• Parameter estimation and model fitting
• Volatility forecasting
• Model diagnostics and statistical metrics
• Support for time-indexed data

Usage

Add this to your Cargo.toml:

[dependencies]
oxidiviner-garch = "0.1.0"

Example

use oxidiviner_garch::GARCHModel;

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // Create a GARCH(1,1) model
    let mut model = GARCHModel::new(1, 1, None)?;
    
    // Sample time series data
    let data = vec![0.1, 0.2, -0.3, 0.1, -0.2, 0.3, -0.1, 0.4, -0.2, 0.1];
    
    // Fit the model
    model.fit(&data, None)?;
    
    // Display model parameters
    println!("{}", model);
    
    // Forecast future volatility (5 steps ahead)
    let forecast = model.forecast_variance(5)?;
    println!("Volatility forecast: {:?}", forecast);
    
    Ok(())
}

Model Definition

The GARCH(p,q) model is defined as:

y_t = μ + ε_t
ε_t = σ_t * z_t, where z_t ~ N(0,1)
σ²_t = ω + Σ(i=1 to p) α_i * ε²_{t-i} + Σ(j=1 to q) β_j * σ²_{t-j}

Where:

• p is the order of the ARCH terms (ε²)
• q is the order of the GARCH terms (σ²)
• ω is the constant term (omega)
• α_i are the ARCH parameters
• β_j are the GARCH parameters

License

Licensed under the MIT License. See LICENSE for details.