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Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models

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  • Jan Beran
  • Yuanhua Feng
  • Sucharita Ghosh

Abstract

Duration series often exhibit long-range dependence and local nonstationarities. Here, exponential FARIMA (EFARIMA) and exponential SEMIFAR (ESEMIFAR) models are introduced. These models capture simultaneously nonstationarities in the mean as well as short- and long-range dependence, while avoiding the complication of unobservable latent processes. The models can be thought of as locally stationary long-memory extensions of exponential ACD models. Statistical properties of the models are derived. In particular the long-memory parameter in the original and the log-transformed process is the same. For Gaussian innovations, exact explicit formulas for all moments and autocovariances are given, and the unconditional distribution is log-normal. Estimation and model selection can be carried out with standard software. The approach is illustrated by an application to average daily transaction durations. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Jan Beran & Yuanhua Feng & Sucharita Ghosh, 2015. "Modelling long-range dependence and trends in duration series: an approach based on EFARIMA and ESEMIFAR models," Statistical Papers, Springer, vol. 56(2), pages 431-451, May.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:2:p:431-451
    DOI: 10.1007/s00362-014-0590-x
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    Cited by:

    1. Sucarrat, Genaro, 2018. "The Log-GARCH Model via ARMA Representations," MPRA Paper 100386, University Library of Munich, Germany.
    2. Lihong Wang, 2020. "Lack of fit test for long memory regression models," Statistical Papers, Springer, vol. 61(3), pages 1043-1067, June.
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    4. 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.
    5. Feng, Yuanhua & Zhou, Chen, 2015. "Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD," International Journal of Forecasting, Elsevier, vol. 31(2), pages 349-363.
    6. Lihong Wang, 2020. "Nearest neighbors estimation for long memory functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 709-725, December.
    7. Yuanhua Feng & Jan Beran & Sebastian Letmathe, 2021. "An extended exponential SEMIFAR model with application in R," Working Papers CIE 145, Paderborn University, CIE Center for International Economics.
    8. Sebastian Letmathe, 2022. "Data-driven P-Splines under short-range dependence," Working Papers CIE 152, Paderborn University, CIE Center for International Economics.
    9. 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.

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