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Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions

Author

Listed:
  • A. Gregorio

    (“Sapienza” University of Rome)

  • S. M. Iacus

    (University of Milan)

Abstract

The aim of this paper is to introduce a new type of test statistic for simple null hypothesis on one-dimensional ergodic diffusion processes sampled at discrete times. We deal with a quasi-likelihood approach for stochastic differential equations (i.e. local gaussian approximation of the transition functions) and define a test statistic by means of the empirical $$L^2$$ L 2 -distance between quasi-likelihoods. We prove that the introduced test statistic is asymptotically distribution free; namely it weakly converges to a $$\chi ^2$$ χ 2 random variable. Furthermore, we study the power under local alternatives of the parametric test. We show by the Monte Carlo analysis that, in the small sample case, the introduced test seems to perform better than other tests proposed in literature.

Suggested Citation

  • A. Gregorio & S. M. Iacus, 2019. "Empirical $$L^2$$ L 2 -distance test statistics for ergodic diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 233-261, July.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:2:d:10.1007_s11203-018-9176-x
    DOI: 10.1007/s11203-018-9176-x
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    References listed on IDEAS

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    1. Morales, D. & Pardo, L. & Vajda, I., 1997. "Some New Statistics for Testing Hypotheses in Parametric Models, ," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 137-168, July.
    2. De Gregorio, Alessandro & Maria Iacus, Stefano, 2010. "Clustering of discretely observed diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 598-606, February.
    3. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    4. Iacus, Stefano M. & Yoshida, Nakahiro, 2012. "Estimation for the change point of volatility in a stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1068-1092.
    5. Iacus, Stefano Maria & Uchida, Masayuki & Yoshida, Nakahiro, 2009. "Parametric estimation for partially hidden diffusion processes sampled at discrete times," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1580-1600, May.
    6. Yoshida, Nakahiro, 1992. "Estimation for diffusion processes from discrete observation," Journal of Multivariate Analysis, Elsevier, vol. 41(2), pages 220-242, May.
    7. Kengo Kamatani & Masayuki Uchida, 2015. "Hybrid multi-step estimators for stochastic differential equations based on sampled data," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 177-204, July.
    8. Masayuki Uchida & Nakahiro Yoshida, 2014. "Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 181-219, July.
    9. De Gregorio, Alessandro & Iacus, Stefano M., 2012. "Adaptive Lasso-Type Estimation For Multivariate Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 28(4), pages 838-860, August.
    10. Phillips, Peter C.B. & Yu, Jun, 2009. "A two-stage realized volatility approach to estimation of diffusion processes with discrete data," Journal of Econometrics, Elsevier, vol. 150(2), pages 139-150, June.
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    Cited by:

    1. Yusuke Kaino & Shogo H. Nakakita & Masayuki Uchida, 2020. "Hybrid estimation for ergodic diffusion processes based on noisy discrete observations," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 171-198, April.

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