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Inference in generalized exponential O–U processes

Author

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  • Yunhong Lyu

    (University of Windsor)

  • Sévérien Nkurunziza

    (University of Windsor)

Abstract

In this paper, we consider an inference problem in generalized exponential Ornstein–Uhlenbeck processes. Salient features of this paper consists in the fact that, first, we generalized the classical exponential Ornstein–Uhlenbeck processes to the case where the drift coefficient is driven by a period function of time. Second, as opposed to the results in recent literature, the dimension of the drift parameter is considered as unknown. Third, we weaken some assumptions, in recent literature, underlying the asymptotic optimality of some estimators of the drift parameter. We propose the unrestricted maximum likelihood estimator, the restricted maximum likelihood estimator and some shrinkage estimators for the drift parameters. We also derive asymptotic distributional risk of the proposed estimators as well as their relative efficiency. Finally, we present the simulation results which corroborate the theoretical findings.

Suggested Citation

  • Yunhong Lyu & Sévérien Nkurunziza, 2023. "Inference in generalized exponential O–U processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 581-618, October.
    • Handle: RePEc:spr:sistpr:v:26:y:2023:i:3:d:10.1007_s11203-023-09291-1
    DOI: 10.1007/s11203-023-09291-1
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    References listed on IDEAS

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    1. Jaume Masoliver & Josep Perello, 2006. "Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 423-433.
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    3. Fuqi Chen & Rogemar Mamon & Sévérien Nkurunziza, 2018. "Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 807-853, August.
    4. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    5. Sévérien Nkurunziza & Pei Patrick Zhang, 2018. "Estimation and testing in generalized mean-reverting processes with change-point," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 191-215, April.
    6. Jaime Casassus & Pierre Collin‐Dufresne, 2005. "Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates," Journal of Finance, American Finance Association, vol. 60(5), pages 2283-2331, October.
    7. Herold Dehling & Brice Franke & Thomas Kott, 2010. "Drift estimation for a periodic mean reversion process," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 175-192, October.
    8. Josep Perello & Ronnie Sircar & Jaume Masoliver, 2008. "Option pricing under stochastic volatility: the exponential Ornstein-Uhlenbeck model," Papers 0804.2589, arXiv.org, revised May 2008.
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