## A test for model specification of diffusion processes.(English)Zbl 1132.62063

Summary: We propose a test for model specification of a parametric diffusion process based on kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing bandwidth, which is effectively a Studentized $$L_{2}$$-distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process. To reduce the sensitivity of the test to smoothing bandwidth choice, the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths. To better capture the finite sample distribution of the test statistic and data dependence, the critical value of the test is obtained by a parametric bootstrap procedure. Properties of the test are evaluated asymptotically and numerically by simulation and by a real data example.

### MSC:

 62M02 Markov processes: hypothesis testing 62G07 Density estimation 62F40 Bootstrap, jackknife and other resampling methods 65C60 Computational problems in statistics (MSC2010)
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### References:

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