Smooth Transition HYGARCH Model: Stability and Forecasting

TL;DR

The paper introduces the ST-HYGARCH model to capture smooth transitions in long-memory volatility processes, demonstrating its stability and superior forecasting performance over traditional HYGARCH in financial time series.

Contribution

It proposes the novel ST-HYGARCH model, analyzes its asymptotic properties, develops a score test for smooth transition, and validates its effectiveness on S&P 500 data.

Findings

ST-HYGARCH outperforms HYGARCH in forecasting accuracy.

The model captures phase transitions in volatility effectively.

Simulation confirms the asymptotic properties and test validity.

Abstract

HYGARCH process is the commonly used long memory process in modeling the long-rang dependence in volatility. Financial time series are characterized by transition between phases of different volatility levels. The smooth transition HYGARCH (ST-HYGARCH) model is proposed to model time-varying structure with long memory property. The asymptotic behavior of the second moment is studied and an upper bound for it is derived. A score test is developed to check the smooth transition property. The asymptotic behavior of the proposed model and the score test is examined by simulation. The proposed model is applied to the \textit{S}\&\textit{P}500 indices for some period which show evidence of smooth transition property and demonstrates out-performance of the ST-HYGARCH than HYGARCH in forecasting.