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Conditional Distributions of Mandelbrot–van ness Fractional LÉVY Processes and Continuous-Time ARMA–GARCH-Type Models with Long Memory

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  • Holger Fink

Abstract

type="main" xml:id="jtsa12135-abs-0001"> Long-memory effects can be found in many data sets from finance to hydrology. Therefore, models that can reflect these properties have become more popular in recent years. Mandelbrot–Van Ness fractional Lévy processes allow for such stationary long-memory effects in their increments and have been used in different settings ranging from fractionally integrated continuous-time ARMA–GARCH-type setups to general stochastic differential equations. However, their conditional distributions have not yet been considered in detail. In this article, we provide a closed formula for their conditional characteristic functions and suggest several applications to continuous-time ARMA–GARCH-type models with long memory.

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  • Holger Fink, 2016. "Conditional Distributions of Mandelbrot–van ness Fractional LÉVY Processes and Continuous-Time ARMA–GARCH-Type Models with Long Memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 30-45, January.
    • Handle: RePEc:bla:jtsera:v:37:y:2016:i:1:p:30-45
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    File URL: http://hdl.handle.net/10.1111/jtsa.12135
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    References listed on IDEAS

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    1. Christian Bender & Tommi Sottinen & Esko Valkeila, 2008. "Pricing by hedging and no-arbitrage beyond semimartingales," Finance and Stochastics, Springer, vol. 12(4), pages 441-468, October.
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    3. Marquardt, Tina, 2007. "Multivariate fractionally integrated CARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1705-1725, October.
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    Cited by:

    1. Fink, Holger & Schlüchtermann, Georg, 2018. "Fractional Lévy Cox–Ingersoll–Ross and Jacobi processes," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 84-91.

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