Modeling 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 their ability to capture the features of volatility clustering and long-memory persistence. However, in the presence of structural changes, it is well known that the estimate of long memory will be spurious. Consequently, two modeling approaches are developed to incorporate structural changes into the FIGARCH framework. One approach is to model the intercept in the conditional variance equation via a certain function of time. Based on this approach, the Adaptive-FIGARCH (A-FIGARCH) and Time-Varying FIGARCH (TV-FIGARCH) models are proposed. The second approach is to model the time-series in separate stages. In the first stage, a certain algorithm is applied to detect the change points. The FIGARCH model is fitted to the time-series in the next stage, with the intercept (and other parameters) being allowed to vary between change points. An example of a recently developed algorithm for detecting change points is the Nonparametric Change Point Model (NPCPM), which can be readily applied to the standard FIGARCH framework (NPCPM-FIGARCH). In this paper, we adopt the second approach but use the 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 is compared with other FIGARCH-type models via Monte-Carlo simulations and high-frequency datasets. From the comparison, we find that the 3S-FIGARCH model can largely improve the fit and potentially lead to a more reliable estimator of the long-memory parameter.