A simulation-based specification test for diffusion processes

Geetesh Bhardwaj, Valentina Corradi, Norman R. Swanson

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This article makes two contributions. First, we outline a simple simulation-based framework for constructing conditional distributions for multifactor and multidimensional diffusion processes, for the case where the functional form of the conditional density is unknown. The distributions can be used, for example, to form predictive confidence intervals for time period t + τ, given information up to period t. Second, we use the simulation-based approach to construct a test for the correct specification of a diffusion process. The suggested test is in the spirit of the conditional Kolmogorov test of Andrews. However, in the present context the null conditional distribution is unknown and is replaced by its simulated counterpart. The limiting distribution of the test statistic is not nuisance parameter-free. In light of this, asymptotically valid critical values are obtained via appropriate use of the block bootstrap. The suggested test has power against a larger class of alternatives than tests that are constructed using marginal distributions/ densities. The findings of a small Monte Carlo experiment underscore the good finite sample properties of the proposed test, and an empirical illustration underscores the ease with which the proposed simulation and testing methodology can be applied.

Original languageEnglish (US)
Pages (from-to)176-193
Number of pages18
JournalJournal of Business and Economic Statistics
Issue number2
StatePublished - Apr 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


  • Block bootstrap
  • Continuous time model
  • Finance
  • Parameter estimation error
  • Simulated GMM
  • Stochastic volatility


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