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A Generalized ARFIMA Process with Markov-Switching Fractional Differencing Parameter

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Listed:
  • Wen-Jen Tsay
  • Wolfgang Härdle

Abstract

We propose a general class of Markov-switching-ARFIMA processes in order to combine strands of long memory and Markov-switching literature. Although the coverage of this class of models is broad, we show that these models can be easily estimated with the DLV algorithm proposed. This algorithm combines the Durbin-Levinson and Viterbi procedures. A Monte Carlo experiment reveals that the finite sample performance of the proposed algorithm for a simple mixture model of Markov-switching mean and ARFIMA(1, d, 1) process is satisfactory. We apply the Markov-switching-ARFIMA models to the U.S. real interest rates, the Nile river level, and the U.S. unemployment rates, respectively. The results are all highly consistent with the conjectures made or empirical results found in the literature. Particularly, we confirm the conjecture in Beran and Terrin (1996) that the observations 1 to about 100 of the Nile river data seem to be more independent than the subsequent observations, and the value of differencing parameter is lower for the first 100 observations than for the subsequent data.

Suggested Citation

  • 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.
  • Handle: RePEc:hum:wpaper:sfb649dp2007-022
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2007-022.pdf
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    References listed on IDEAS

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    1. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    2. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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    Cited by:

    1. repec:jfr:ijfr11:v:8:y:2017:i:4:p:148-166 is not listed on IDEAS
    2. Massimiliano Caporin & Rangan Gupta, 2017. "Time-varying persistence in US inflation," Empirical Economics, Springer, vol. 53(2), pages 423-439, September.
    3. Guglielmo Maria Caporale & Luis Gil-Alana, 2012. "Long Memory and Volatility Dynamics in the US Dollar Exchange Rate," Multinational Finance Journal, Multinational Finance Journal, vol. 16(1-2), pages 105-136, March - J.
    4. Pierre Perron & Rasmus T. Varneskov, 2011. "Combining Long Memory and Level Shifts in Modeling and Forecasting the Volatility of Asset Returns," Boston University - Department of Economics - Working Papers Series WP2011-050, Boston University - Department of Economics.
    5. Volodymyr Perederiy, 2007. "Kombinierte Liquiditäts- und Solvenzkennzahlen und ein darauf basierendes Insolvenzprognosemodell für deutsche GmbHs," SFB 649 Discussion Papers SFB649DP2007-060, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. repec:bpj:jtsmet:v:10:y:2018:i:1:p:20:n:1 is not listed on IDEAS
    7. Chen, Shyh-Wei, 2013. "Long memory and regime switching properties of current account deficits in the US," Economic Modelling, Elsevier, vol. 35(C), pages 78-87.

    More about this item

    Keywords

    Markov chain; ARFIMA process; Viterbi algorithm; Long memory.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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