关键词: 函数型金融时间序列, EGARCH, 非对称性, 波动率

Abstract: The traditional functional GARCH-type models can be used to describe the heteroscedasticity of functional financial time series, but they have the following drawbacks: Firstly, they don’t consider the asymmetry of volatility; Secondly, they can not explain whether the shock of current information to future conditional variance persists or not; Thirdly, the condition of non-negative parameter may limit the dynamics of conditional volatility. Considering these, this paper, on the basis of EGARCH model, proposes a functional EGARCH model (f EGARCH model), gives the specific steps of its least square estimation and quasi-maximum likelihood estimation, and derives the news impact curve (NIC) and formula of cumulative impact response ratio function (CIRR). Monte Carlo simulation shows that the model can capture the asymmetry, and its quasi-maximum likelihood method is more effective than the least square estimation method. After we apply f EGARCH to CSI 300 index, NIC shows that the model can capture the asymmetry of volatility, and CIRR indicates that the impact of current returns on future volatility is highly persistent. Finally, the DM test based on quasi-maximum likelihood, the SPA test and the MCS test based on several robust loss functions show that the fEGARCH model has better prediction accuracy than the functional GARCH model (fGARCH model).

Key words: Functional Financial Time Series, EGARCH, Asymmetry, Volatility