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On the goodness-of-fit testing for ergodic diffusion processes

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  • Yury Kutoyants

Abstract

We consider the goodness-of-fit testing problem for ergodic diffusion processes. The basic hypothesis is supposed to be simple. The diffusion coefficient is known and the alternatives are described by the different trend coefficients. We study the asymptotic distribution of the Cramér–von Mises type tests based on the empirical distribution function and local time estimator of the invariant density. Particularly, we propose a transformation which makes these tests asymptotically distribution-free.

Suggested Citation

  • Yury Kutoyants, 2010. "On the goodness-of-fit testing for ergodic diffusion processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 529-543.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:4:p:529-543
    DOI: 10.1080/10485250903359564
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    Cited by:

    1. Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    2. Yury Kutoyants, 2012. "On identification of the threshold diffusion processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 383-413, April.
    3. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    4. Yury Kutoyants, 2014. "On asymptotic distribution of parameter free tests for ergodic diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 17(2), pages 139-161, July.

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