# On Time-Varying Amplitude HGARCH Mode

## TL;DR

This paper introduces a novel HGARCH model with time-varying amplitude, demonstrating its stability and improved forecasting performance for financial volatility compared to existing models.

## Contribution

The paper proposes a new HGARCH model with a time-varying amplitude feature and develops a score test for its behavior, enhancing volatility modeling accuracy.

## Key findings

- The model is stable under certain conditions.
- It outperforms HGARCH and FIGARCH models in SP500 volatility forecasting.
- The score test effectively detects time-varying amplitude in the model.

## Abstract

The HGARCH model allows long-memory impact in volatilities. A new HGARCH model with time-varying amplitude is considered in this paper. We show the stability of the model as well. A score test is introduced to check the time-varying behavior in amplitude. Some value-at-risk tests are applied to evaluate the forecastings. Simulations are provided which provide further support to the proposed model. We have also have shown the competative performance of our model in forecasting, by compairing it with HGARH and FIGARCH models for some period of SP500 indices.