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

Author

Listed:
  • Yuanhua Feng

    (Paderborn University)

  • Jan Beran

    (University of Konstanz)

  • Sebastian Letmathe

    (Paderborn University)

  • Sucharita Ghosh

    (Swiss Federal Research Institute WSL)

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.

Suggested Citation

  • Yuanhua Feng & Jan Beran & Sebastian Letmathe & Sucharita Ghosh, 2020. "Fractionally integrated Log-GARCH with application to value at risk and expected shortfall," Working Papers CIE 137, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:137
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    References listed on IDEAS

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    Cited by:

    1. Yuanhua Feng & Thomas Gries & Sebastian Letmathe, 2023. "FIEGARCH, modulus asymmetric FILog-GARCH and trend-stationary dual long memory time series," Working Papers CIE 156, Paderborn University, CIE Center for International Economics.
    2. Sebastian Letmathe & Yuanhua Feng & André Uhde, 2021. "Semiparametric GARCH models with long memory applied to Value at Risk and Expected Shortfall," Working Papers CIE 141, Paderborn University, CIE Center for International Economics.

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    More about this item

    Keywords

    FI-Log-GARCH; stationary solutions; finite fourth moments; covariance structure; rolling forecasting VaR and ES; traffic light test of ES;
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