This paper has to do with a Cramér-von Mises test for symmetry of the error distribution in a class of absolutely regular and non-necessarily stationary heteroscedastic models. The test statistic is based on the empirical characteristic function. Its convergence, as well as that of the...

We consider a diffusion process (X <Subscript> t </Subscript>)<Subscript> t ≥ 0</Subscript>, with drift b(x) and diffusion coefficient σ(x). At discrete times t <Subscript> k </Subscript> = k δ for k from 1 to M, we observe noisy data of the sample path, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${Y_{k\delta}=X_{k\delta}+\varepsilon_{k}}$$</EquationSource > </InlineEquation> . The random variables <InlineEquation ID="IEq2"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></subscript></subscript></subscript>

Identifying a model by the penalized contrast procedure, we give an analytical estimation of misfitting subsets in the specific case of a least squares contrast. Then, specifying the statistical model, this allows to determine penalization rates ensuring a consistent identification. Applications...

We consider the model selection problem for ergodic diffusion processes based on sampled data. The adaptive estimators for parameters of drift and diffusion coefficients are used in order to construct Akaike’s information criterion (AIC) type model selection statistics. Asymptotic properties...