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Goodness-of-fit test for ergodic diffusions by discrete-time observations: an innovation martingale approach

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  • Hiroki Masuda
  • Ilia Negri
  • Yoichi Nishiyama

Abstract

We consider a nonparametric goodness-of-fit test problem for the drift coefficient of one-dimensional ergodic diffusions. Our test is based on the discrete-time observation of the processes, and the diffusion coefficient is a nuisance function which is estimated in some sense in our testing procedure. We prove that the limit distribution of our test is the supremum of the standard Brownian motion, and thus our test is asymptotically distribution free. We also show that our test is consistent under any fixed alternatives.

Suggested Citation

  • Hiroki Masuda & Ilia Negri & Yoichi Nishiyama, 2011. "Goodness-of-fit test for ergodic diffusions by discrete-time observations: an innovation martingale approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 237-254.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:237-254
    DOI: 10.1080/10485252.2010.510186
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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. Monsalve-Cobis, Abelardo & González-Manteiga, Wenceslao & Febrero-Bande, Manuel, 2011. "Goodness-of-fit test for interest rate models: An approach based on empirical processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3073-3092, December.

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