Title: Moment and memory properties of exponential-type conditional heteroscedasticity models
Authors: James Davidson - University of Exeter (United Kingdom)
Xiaoyu Li - Capital University of Economics and Business (China) [presenting]
Abstract: The aim is to investigate the moment and memory properties of exponential-type conditional heteroscedasticity models, including exponential generalised autoregressive conditional heteroscedastic (EGARCH) and the fractionally integrated (FIEGARCH(BM)). The moment conditions of these models are derived from previous literature, and the memory properties are measured by using a near-epoch dependence (NED) functions of an independent process approach. The existence of moments supports the limited memory properties of these models. It is shown that the exponential autoregressive conditional heteroscedastic (EARCH)($\infty$) processes may exhibit geometric memory, hyperbolic memory or long memory. A general expression of the HY/FIEGARCH(DL) model is introduced depending on the properties of the lag coefficients, and the simulation results show that the HYEGARCH model has a hyperbolic memory and the FIEGARCH(DL) model exhibits long memory in the absolute return series. The functional central limit theorem (FCLT) or fractional FCLT for the partial sum of the processes in the EGARCH-type models is also derived.