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A Generalized ARFIMA Model with Smooth Transition Fractional Integration Parameter

Author

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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

    as
    1. Aloy Marcel & Dufrénot Gilles & Tong Charles Lai & Peguin-Feissolle Anne, 2013. "A smooth transition long-memory model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(3), pages 281-296, May.
    2. Alvarez-Ramirez, Jose & Alvarez, Jesus & Solis, Ricardo, 2010. "Crude oil market efficiency and modeling: Insights from the multiscaling autocorrelation pattern," Energy Economics, Elsevier, vol. 32(5), pages 993-1000, September.
    3. Gilles Dufrenot & Dominique Guegan & Anne Peguin-Feissolle, 2008. "Changing-regime volatility: a fractionally integrated SETAR model," Applied Financial Economics, Taylor & Francis Journals, vol. 18(7), pages 519-526.
    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. Engelen, Steve & Norouzzadeh, Payam & Dullaert, Wout & Rahmani, Bahareh, 2011. "Multifractal features of spot rates in the Liquid Petroleum Gas shipping market," Energy Economics, Elsevier, vol. 33(1), pages 88-98, January.
    6. Gilles DUFRENOT & Dominique GUEGAN & Anne PEGUIN-FEISSOLLE, 2003. "A SETAR model with long-memory dynamics," Econometrics 0309002, University Library of Munich, Germany.
    7. 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.
    8. Tsay, Wen-Jen & Härdle, Wolfgang Karl, 2007. "A generalized ARFIMA process with Markov-switching fractional differencing parameter," SFB 649 Discussion Papers 2007-022, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. 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.
    10. repec:hum:wpaper:sfb649dp2007-022 is not listed on IDEAS
    11. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
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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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