# Seasonal FIEGARCH Processes

## TL;DR

This paper introduces the seasonal FIEGARCH (SFIEGARCH) process, establishing its theoretical properties, analyzing its dependence structure, and demonstrating its application to model S&P 500 stock index volatility.

## Contribution

The paper develops the theory of SFIEGARCH processes, including conditions for existence, stationarity, invertibility, and ergodicity, and applies it to real financial data.

## Key findings

- SFIEGARCH processes exhibit specific autocovariance and autocorrelation structures.
- Application to S&P 500 data demonstrates the model's effectiveness in volatility analysis.
- Graphical illustrations support the theoretical properties of SFIEGARCH.

## Abstract

Here we develop the theory of seasonal FIEGARCH processes, denoted by SFIEGARCH, establishing conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We analyze their asymptotic dependence structure by means of the autocovariance and autocorrelation functions. We also present some properties regarding their spectral representation. All properties are illustrated through graphical examples and an application of SFIEGARCH models to describe the volatility of the S&P500 US stock index log-return time series in the period from December 13, 2004 to October 10, 2009 is provided.