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Fractional Ornstein–Uhlenbeck processes. Joseph effect in models with infinite variance

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  • Magdziarz, Marcin

Abstract

We consider five fractional generalizations of the Markovian α-stable Ornstein–Uhlenbeck process and explore the dependence structure of these stochastic models. Since the variance of α-stable distributed random variables is infinite, we describe the dependence structure of the introduced processes in the language of the function called codifference. We present exact formulas for the asymptotic behavior of codifference and answer the question of long-range dependence property (Joseph effect) for the discussed fractional α-stable models. We show that the fractional Ornstein–Uhlenbeck processes can display both Noah and Joseph effect.

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  • Magdziarz, Marcin, 2008. "Fractional Ornstein–Uhlenbeck processes. Joseph effect in models with infinite variance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 123-133.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:1:p:123-133
    DOI: 10.1016/j.physa.2007.08.016
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    1. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401, December.
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    Cited by:

    1. Xiao, Weilin & Zhang, Weiguo & Zhang, Xili & Chen, Xiaoyan, 2014. "The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 320-337.
    2. Marko Voutilainen & Lauri Viitasaari & Pauliina Ilmonen & Soledad Torres & Ciprian Tudor, 2022. "Vector‐valued generalized Ornstein–Uhlenbeck processes: Properties and parameter estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 992-1022, September.

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