HAR-CAESar Documentation

HAR-CAESar (Heterogeneous Autoregressive Conditional Autoregressive Expected Shortfall) is a Python framework for forecasting joint Value at Risk (VaR) and Expected Shortfall (ES).

This library implements the models developed for the MSc Thesis: “Forecasting Tail Risk with Long-Memory: A Heterogeneous Extension of the CAESar Model”. _.

Key Features

  • Long-Memory Modeling: Captures volatility cascades using HAR dynamics at daily, weekly, and monthly horizons

  • Asymmetric Slope Effects: Separates positive and negative return impacts to capture leverage effects

  • Joint Estimation: Simultaneous VaR and ES forecasting using the Fissler-Ziegel loss function

  • Comprehensive Backtesting: Implements Kupiec, Christoffersen, McNeil-Frey, and Acerbi-Szekely tests

  • Benchmarks: Includes CAESar, CAViaR, GAS1, and GAS2 implementations for comparison

Quick Start

Install the package:

git clone https://github.com/shawcharles/HAR-CAESar.git
cd HAR-CAESar
pip install -e .

Basic usage example:

import numpy as np
from har_caesar import HAR_CAESar

# Generate data
y = np.random.normal(0, 1, 2000)

# Fit model and predict
model = HAR_CAESar(theta=0.025)
results = model.fit_predict(y, ti=1500, seed=42)

# Access forecasts
var_forecasts = results['qf']
es_forecasts = results['ef']

Documentation Contents

Indices and tables