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A model specification test for nonlinear stochastic diffusions with delay

Author

Listed:
  • Zongwu Cai

    (The University of Kansas)

  • Hongwei Mei

    (Texas Tech University)

  • Rui Wang

    (The University of Kansas)

Abstract

This paper investigates model specification problems for nonlinear stochastic differential equations with delay (SDDE). Compared to the model specification for conventional stochastic diffusions without delay, the observed sequence does not admit a Markovian structure so that the classical testing procedures may not be applicable. To overcome this difficulty, a moment estimator is newly proposed based on the ergodicity of SDDEs and its asymptotic properties are established. Based on the proposed moment estimator, a testing procedure is proposed for our model specification testing problems. Particularly, the limiting distributions of the proposed test statistic are derived under null hypotheses and the test power is examined under some specific alternative hypotheses. Finally, a Monte Carlo simulation is conducted to illustrate the finite sample performance of the proposed test.

Suggested Citation

  • Zongwu Cai & Hongwei Mei & Rui Wang, 2024. "A model specification test for nonlinear stochastic diffusions with delay," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 795-812, October.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:3:d:10.1007_s11203-024-09309-2
    DOI: 10.1007/s11203-024-09309-2
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    References listed on IDEAS

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    1. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    2. Ilia Negri & Yoichi Nishiyama, 2009. "Goodness of fit test for ergodic diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 919-928, December.
    3. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    4. Uwe Küchler & Michael Sørensen, 2010. "A simple estimator for discrete-time samples from affine stochastic delay differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 125-132, June.
    5. M. Kleptsyna & Yu. Kutoyants, 2014. "On asymptotically distribution free tests with parametric hypothesis for ergodic diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 295-319, October.
    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    7. Aït-Sahalia, Yacine & Fan, Jianqing & Peng, Heng, 2009. "Nonparametric Transition-Based Tests for Jump Diffusions," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1102-1116.
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