# Markov Switch Smooth Transition HYGARCH Model: Stability and Estimation

## TL;DR

This paper introduces a novel Markov switch smooth-transition HYGARCH model that captures complex volatility dynamics, including long-range dependence, with stability analysis and Bayesian estimation, demonstrating improved forecasting performance on financial data.

## Contribution

It proposes a new flexible HYGARCH-based model with Markov switching and smooth transition features, along with stability conditions and Bayesian estimation methods.

## Key findings

- Model effectively captures different volatility regimes.
- Bayesian estimation via Gibbs sampling is successful.
- Model outperforms existing HYGARCH models in forecasts.

## Abstract

HYGARCH model is basically used to model long-range dependence in volatility. We propose Markov switch smooth-transition HYGARCH model, where the volatility in each state is a time-dependent convex combination of GARCH and FIGARCH. This model provides a flexible structure to capture different levels of volatilities and also short and long memory effects. The necessary and sufficient condition for the asymptotic stability is derived. Forecast of conditional variance is studied by using all past information through a parsimonious way. Bayesian estimations based on Gibbs sampling are provided. A simulation study has been given to evaluate the estimations and model stability. The competitive performance of the proposed model is shown by comparing it with the HYGARCH and smooth-transition HYGARCH models for some period of the \textit{S}\&\textit{P}500 indices based on volatility and value-at-risk forecasts.