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Doubly fractional models for dynamic heteroscedastic cycles

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  • Artiach, Miguel
  • Arteche, Josu

Abstract

Strong cyclical persistence is a common phenomenon that has been documented not only in the levels but also in the volatility of many time series, specially in astronomical or business cycle data. The class of doubly fractional models is extended to include the possibility of long memory in cyclical (non-zero) frequencies in both levels and volatility, and a new model, the GARMA–GARMASV (Gegenbauer AutoRegressive Moving Average–Gegenbauer AutoRegressive Moving Average 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, Miguel & Arteche, Josu, 2012. "Doubly fractional models for dynamic heteroscedastic cycles," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2139-2158.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:2139-2158
    DOI: 10.1016/j.csda.2011.10.018
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    Cited by:

    1. Shelton Peiris & Manabu Asai & Michael McAleer, 2017. "Estimating and Forecasting Generalized Fractional Long Memory Stochastic Volatility Models," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 10(4), pages 1-16, December.
    2. Manabu Asai & Shelton Peiris & Michael McAleer, 2017. "Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory," Documentos de Trabajo del ICAE 2017-26, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.

    More about this item

    Keywords

    Stochastic volatility; Cycles; Long memory; QML estimation; Sunspot index;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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