Adaptive Realized Hyperbolic GARCH Process: Stability and Estimation

TL;DR

This paper introduces an adaptive hyperbolic GARCH model that captures long memory and structural breaks in high-frequency financial data, with stability analysis and simulation validation.

Contribution

It proposes a novel adaptive realized hyperbolic GARCH model incorporating structural change and stability conditions, advancing modeling of complex financial time series.

Findings

The model effectively captures long memory and structural breaks.

Simulation studies show improved performance over existing models.

Stability conditions are rigorously derived and validated.

Abstract

In this paper, we propose an Adaptive Realized Hyperbolic GARCH (A-Realized HYGARCH) process to model the long memory of high-frequency time series with possible structural breaks. The structural change is modeled by allowing the intercept to follow the smooth and flexible function form introduced by Gallant (1984). In addition, stability conditions of the process are investigated. A Monte Carlo study is investigated in order to illustrate the performance of the A-Realized HYGARCH process compared to the Realized HYGARCH with or without structural change.