Modelling High-Frequency Volatility with Three-State FIGARCH Models

Abstract

Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity (FIGARCH) models have enjoyed considerable popularity over the past decade because of its ability to capture the volatility clustering and estimate long memory of conditional volatility. However, when structural breaks are present, it is well known that the estimate of long memory will be spurious. Consequently, two approaches are developed to incorporate the structural breaks into FIGARCH framework. First, the intercept in the conditional variance equation is modelled via a certain function of time. The Adaptive-FIGARCH (A-FIGARCH) and Time-Varying FIGARCH (TV-FIGARCH) models are proposed based on this idea. Second, financial series are modelled in separate stages. At the first stage, certain algorithm is applied to detect the change points. FIGARCH model is then fitted, with the intercept (and other parameters) being allowed to vary between change points. A recently developed such algorithm Nonparametric Change Point Model (NPCPM) can be extended to the FIGARCH framework, which is the NPCPM-FIGARCH model. We adopt the second approach but use Markov Regime-Switching (MRS) model to detect the change points and identify three economic states depending on the scale of volatility. This new 2-stage Three-State FIGARCH (3S-FIGARCH) framework and other FIGARCH models are fitted to the hourly data set composed of four major stock indexes, with Gaussian and non-Gaussian distribution assumptions, individually. From the comparison, we find that our model can potentially give an improved fit with better estimate of long memory parameter.