Nonparametric transition-based tests for jump diffusions

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)1102-1116
Number of pages15
JournalJournal of the American Statistical Association
Volume104
Issue number487
DOIs
StatePublished - Jan 1 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Generalized likelihood ratio test
  • Jump diffusion
  • Local linear fit
  • Markovian process
  • Null distribution
  • Specification test
  • Transition density

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