Nonparametric transition-based tests for diffusions

Yacine At-Sahalia Jianqing Fan Heng Peng

Statistics Theory and Methods mathscidoc:1912.43375

Manuscript, Princeton University, 2009.11
We develop a specification test for the transition density of a discretely-sampled continuous-time diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts assumed by the null hypothesis. We provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions. We establish the asymptotic null distributions of proposed test statistics and compute their power functions. The finite sample properties are critically investigated via simulation studies and are compared with other tests. Our approaches are illustrated by applications to implied volatility data and Treasury bill data.
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  title={Nonparametric transition-based tests for diffusions},
  author={Yacine At-Sahalia, Jianqing Fan, and Heng Peng},
  booktitle={Manuscript, Princeton University},
Yacine At-Sahalia, Jianqing Fan, and Heng Peng. Nonparametric transition-based tests for diffusions. 2009. In Manuscript, Princeton University.
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