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Doubly fractional models for dynamic heteroskedastic cycles

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  • Artiach Escauriaza, Miguel Manuel
  • Arteche González, Jesús María

Abstract

Strong persistence is a common phenomenon that has been documented not only in the levels but also in the volatility of many time series. The class of doubly fractional models is extended to include the possibility of long memory in cyclical (non-zero) frequencies in both the levels and the volatility and a new model, the GARMA-GARMASV (Gegenbauer AutoRegressive Mean Average - Id. Stochastic Volatility) is introduced. A sequential estimation strategy, based on the Whittle approximation to maximum likelihood is proposed and its finite sample performance is evaluated with a Monte Carlo analysis. Finally, a trifactorial in the mean and bifactorial in the volatility version of the model is proved to successfully fit the well-known sunspot index.

Suggested Citation

  • Artiach Escauriaza, Miguel Manuel & Arteche González, Jesús María, 2011. "Doubly fractional models for dynamic heteroskedastic cycles," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    • Handle: RePEc:ehu:biltok:5577
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    References listed on IDEAS

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    1. Zaffaroni, Paolo, 2009. "Whittle estimation of EGARCH and other exponential volatility models," Journal of Econometrics, Elsevier, vol. 151(2), pages 190-200, August.
    2. Zaffaroni, Paolo & d'Italia, Banca, 2003. "Gaussian inference on certain long-range dependent volatility models," Journal of Econometrics, Elsevier, vol. 115(2), pages 199-258, August.
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