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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.

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  • 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," JRFM, MDPI, vol. 10(4), pages 1-16, December.
    2. Asai, Manabu & McAleer, Michael & Peiris, Shelton, 2020. "Realized stochastic volatility models with generalized Gegenbauer long memory," Econometrics and Statistics, Elsevier, vol. 16(C), pages 42-54.
    3. Beaumont, Paul & Smallwood, Aaron, 2019. "Inference for likelihood-based estimators of generalized long-memory processes," MPRA Paper 96313, University Library of Munich, Germany.
    4. Leschinski, Christian & Sibbertsen, Philipp, 2019. "Model order selection in periodic long memory models," Econometrics and Statistics, Elsevier, vol. 9(C), pages 78-94.
    5. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.

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    More about this item

    Keywords

    Stochastic volatility; Cycles; Long memory; QML estimation; Sunspot index;
    All these keywords.

    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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