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Inference in generalized exponential O–U processes with change-point

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 with change-point in the context where the dimensions of the drift parameter are unknown. The proposed method generalizes the work in recent literature for which the change-point has never been considered. Thus, in addition to taking care of possible chock, we study the asymptotic properties of the unrestricted estimator, the restricted estimator, and shrinkage estimators for the drift parameters. We also derive an asymptotic test for change-point detection and we establish the asymptotic distributional risk of the proposed estimators as well as their relative efficiency. Further, we prove that the proposed methods improve the goodness-of-fit. Finally, we present the simulation results which corroborate the theoretical findings and we analyze a financial market data set.

Suggested Citation

  • Yunhong Lyu & Sévérien Nkurunziza, 2024. "Inference in generalized exponential O–U processes with change-point," Statistical Inference for Stochastic Processes, Springer, vol. 27(1), pages 63-102, April.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:1:d:10.1007_s11203-023-09293-z
    DOI: 10.1007/s11203-023-09293-z
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    References listed on IDEAS

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    1. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    2. 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.
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    4. 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.
    5. 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.
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