Fractionally integrated Log-GARCH with application to value at risk and expected shortfall

Yuanhua Feng, Jan Beran (), Sebastian Letmathe and Sucharita Ghosh ()
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Jan Beran: University of Konstanz
Sebastian Letmathe: Paderborn University
Sucharita Ghosh: Swiss Federal Research Institute WSL

No 137, Working Papers CIE from Paderborn University, CIE Center for International Economics

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.

Keywords: FI-Log-GARCH; stationary solutions; finite fourth moments; covariance structure; rolling forecasting VaR and ES; traffic light test of ES (search for similar items in EconPapers)
Pages: 39 pages
Date: 2020-11
New Economics Papers: this item is included in nep-ban, nep-ecm, nep-ets, nep-for and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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