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A Comparative Review of Specification Tests for Diffusion Models

Author

Listed:
  • A. López‐Pérez
  • D. Diz‐Castro
  • M. Febrero‐Bande
  • W. González‐Manteiga

Abstract

Diffusion models play an essential role in modelling continuous‐time stochastic processes in the financial field. Therefore, several proposals have been developed in the last decades to test the specification of stochastic differential equations. We provide a survey to collect some developments on goodness‐of‐fit tests for diffusion models and implement some of these methods to illustrate their finite sample behaviour, regarding size and power, by means of a simulation study. We also apply the ideas of distance covariance to propose a test for the parametric specification of diffusion models, comparing its performance with the other methods and analyzing the effect of the curse of dimensionality. As real data examples, treasury securities with different maturities are considered.

Suggested Citation

  • A. López‐Pérez & D. Diz‐Castro & M. Febrero‐Bande & W. González‐Manteiga, 2026. "A Comparative Review of Specification Tests for Diffusion Models," International Statistical Review, International Statistical Institute, vol. 94(2), pages 347-381, August.
    • Handle: RePEc:bla:istatr:v:94:y:2026:i:2:p:347-381
    DOI: 10.1111/insr.12616
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