Title: Fractionally integrated Log-GARCH with application to value at risk and expected shortfall
Abstract: Volatility modelling is applied in a wide variety of disciplines, namely finance, en- vironment and societal disciplines, where modelling conditional variability is of in- terest e.g. for incremental data. We introduce a new long memory volatility model, called FI-Log-GARCH. Conditions for stationarity and existence of fourth moments are obtained. It is shown that any power of the squared returns shares the same memory parameter. Asymptotic normality of sample means is proved. The practical performance of the proposal is illustrated by an application to one-day rolling forecasts of the VaR (value at risk) and ES (expected shortfall). Comparisons with FIGARCH, FIEGARCH and FIAPARCH models are made using a criterion based on different traffic light test. The results of this paper indicate that the FI-Log- GARCH often outperforms the other models, and thus provides a useful alternative to existing long memory volatility models.
Publication Year: 2020
Publication Date: 2020-01-01
Language: en
Type: preprint
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Cited By Count: 2
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