  Diffusion models play an essential role in modeling 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 these methods to
illustrate their finite sample behavior, regarding size and power, by means of
a simulation study. We also apply the ideas of distance correlation for testing
independence 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.
