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Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD

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  • Yuanhua Feng

    (University of Paderborn)

  • Chen Zhou

    (University of Paderborn)

Abstract

This paper discusses forecasting of long memory and a nonparametric scale function in nonnegative financial processes based on a fractionally integrated Log-ACD (FI-Log-ACD) and its semiparametric extension (Semi-FI-Log-ACD). Necessary and sufficient conditions for the existence of a stationary solution of the FI-Log-ACD are obtained. Properties of this model under log-normal assumption are summarized. A linear predictor based on the truncated AR(oo) form of the logarithmic process is proposed. It is shown that this proposal is an approximately best linear predictor. Approximate variances of the prediction errors for an individual observation and for the conditional mean are obtained. Forecasting intervals for these quantities in the log- and the original processes are calculated under log-normal assumption. The proposals are applied to forecasting daily trading volumes and daily trading numbers in financial market.

Suggested Citation

  • Yuanhua Feng & Chen Zhou, 2013. "Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD," Working Papers CIE 59, Paderborn University, CIE Center for International Economics.
    • Handle: RePEc:pdn:ciepap:59
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    2. Khoo, Zhi De & Ng, Kok Haur & Koh, You Beng & Ng, Kooi Huat, 2025. "Forecasting financial volatility: An approach based on Parkinson volatility measure with long memory stochastic range model," Journal of Empirical Finance, Elsevier, vol. 82(C).
    3. Sucarrat, Genaro, 2018. "The Log-GARCH Model via ARMA Representations," MPRA Paper 100386, University Library of Munich, Germany.
    4. Chiranjit Dutta & Kara Karpman & Sumanta Basu & Nalini Ravishanker, 2023. "Review of Statistical Approaches for Modeling High-Frequency Trading Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 1-48, May.
    5. 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.
    6. Sebastian Letmathe & Jan Beran & Yuanhua Feng, 2024. "An extended exponential SEMIFAR model with application in R," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(22), pages 7914-7926, November.

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