Specification testing in discretized diffusion models: Theory and practice

We propose two new tests for the specification of both the drift and the diffusion functions in a discretized version of a semiparametric continuous–time financial econometric model. Theoretically, we establish some asymptotic consistency results for the proposed tests. Practically, a simple selection procedure for the bandwidth parameter involved in each of the proposed tests is established based on the assessment of the power function of the test under study. To the best of our knowledge, this is the first approach of this kind in specification of continuous–time financial econometrics. The proposed theory is supported by good small and medium–sample studies.