Bootstrap specification tests for diffusion processes

Consistent model-specification tests based on parametric bootstrap

In this paper we establish consistent tests of L2-type for the parametric functional form of the conditional mean of time series with values in Rd. A recent result on asymptotic distributions of U -statistics of weakly dependent observations is invoked to obtain the limit distributions of the test statistics. Since the asymptotic distributions depend on unknown parameters in a complicated way, ...

Bootstrap and permutation tests of independence for point processes

Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general U -statistics, whose corresponding critical values are constructed from bootstrap and randomization/permutation approaches, making as few assumptions as possible on the u...

Specification Tests For The Variance Of A Diffusion

A Test for Model Specification of Diffusion Processes

This paper evaluates the use of the nonparametric kernel method for testing specification of diffusion models as originally considered in Aı̈t-Sahalia (1996). A serious doubt on the ability of the kernel method for diffusion model testing has been cast in Pritsker (1998), who observes severe size distortion of the test proposed by Aı̈t-Sahalia and finds that 2755 years of data are required in ord...

A TEST FOR MODEL SPECIFICATION OF DIFFUSION PROCESSES By Song

Iowa State University, The University of Western Australia and Iowa State University We propose a test for model specification of a parametric diffusion process based on a 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 L2-distance between the kernel t...