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A Generalized ARFIMA Model with Smooth Transition Fractional Integration Parameter

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  • Boubaker Heni

    (IHEC of Sousse, B.P. 40, Route de la ceinture-Sahloul III, 4054, Sousse, Tunisia.)

Abstract

This paper proposes a model of time-varying fractional integration where the long-memory parameter, d$d$ , in an ARFIMA model is allowed to depend on t$t$ and evolve according to a Smooth Transition Regressive (STR) model advanced by Teräsvirta (1994, 1998) . To estimate the time-varying fractional integration parameter, we suggest a new multi-step estimation method based on the wavelet approach using the instantaneous least squares estimator (ILSE). We conduct some simulation experiments and we find that our estimation iterative procedure performs better than that proposed by Boutahar, Dufrénot, and Péguin-Feissolle (2008). An empirical application of this methodology to the volatility of some financial time series is used for illustration purposes. Finally, it is shown that the model proposed offers an interesting framework to describe long-range dependence in the volatility with heterogeneous persistence.

Suggested Citation

  • Boubaker Heni, 2018. "A Generalized ARFIMA Model with Smooth Transition Fractional Integration Parameter," Journal of Time Series Econometrics, De Gruyter, vol. 10(1), pages 1-20, January.
    • Handle: RePEc:bpj:jtsmet:v:10:y:2018:i:1:p:20:n:1
    DOI: 10.1515/jtse-2015-0001
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    References listed on IDEAS

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    1. Jensen, Mark J., 2000. "An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets," Journal of Economic Dynamics and Control, Elsevier, vol. 24(3), pages 361-387, March.
    2. Anne Peguin-Feissolle & Gilles Dufrénot & Dominique Guegan, 2006. "Changing-regime volatility : A fractionally integrated SETAR model," Working Papers halshs-00410540, HAL.
    3. Aloy Marcel & Tong Charles Lai & Peguin-Feissolle Anne & Dufrénot Gilles, 2013. "A smooth transition long-memory model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(3), pages 281-296, May.
    4. Dufrenot, Gilles & Guegan, Dominique & Peguin-Feissolle, Anne, 2005. "Long-memory dynamics in a SETAR model - applications to stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 15(5), pages 391-406, December.
    5. Wen-Jen Tsay & Wolfgang Härdle, 2007. "A Generalized ARFIMA Process with Markov-Switching Fractional Differencing Parameter," SFB 649 Discussion Papers SFB649DP2007-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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    9. Gilles DUFRENOT & Dominique GUEGAN & Anne PEGUIN-FEISSOLLE, 2003. "A SETAR model with long-memory dynamics," Econometrics 0309002, University Library of Munich, Germany.
    10. Mohamed Boutahar & Gilles Dufrénot & Anne Péguin-Feissolle, 2008. "A Simple Fractionally Integrated Model with a Time-varying Long Memory Parameter d t," Computational Economics, Springer;Society for Computational Economics, vol. 31(3), pages 225-241, April.
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    More about this item

    Keywords

    time-varying long memory; local-stationarity; STR model; wavelet; ILSE; financial time series;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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