Nonparametric transition-based tests for jump diffusions

Yacine Ait-Sahalia Jianqing Fan Heng Peng

Statistics Theory and Methods mathscidoc:1912.43308

Journal of the American Statistical Association, 104, (487), 1102-1116, 2009.9
We develop a specification test for the transition density of a discretely sampled continuous-time jump-diffusion process, based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis. As a special case, our method applies to pure diffusions. 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. We investigate the finite-sample properties through simulations and compare them with those of other tests. This article has supplementary material online.
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  title={Nonparametric transition-based tests for jump diffusions},
  author={Yacine Ait-Sahalia, Jianqing Fan, and Heng Peng},
  booktitle={Journal of the American Statistical Association},
Yacine Ait-Sahalia, Jianqing Fan, and Heng Peng. Nonparametric transition-based tests for jump diffusions. 2009. Vol. 104. In Journal of the American Statistical Association. pp.1102-1116.
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