This article presents an equivalence notion of finite order stochastic processes. Local dependence measures are defined in terms of joint and marginal densities. The dependence measures are classified topologically using level sets. The corresponding bifurcation theory is illustrated with some...

For the problem of checking linearity in a heteroscedastic nonparametric regression model under a fixed design assumption we study maximin designs which maximize the minimum power of a nonparametric test over a broad class of alternatives from the assumed linear regression model. It is...

In a recent paper Paparoditis (2000) proposed a new goodness-of-fit test for time series models based on spectral density estimation. The test statistic is based on the distance between a kernel estimator of the ratio of the true and the hypothesized spectral density and the expected value of...

In this note several aspects of specification tests in nonparametric models driven by an absolutely regular process are discussed, which were recently proprosed in the literature. In particular we give a more detailed asymptotic analysis of tests based on kernel methods under fixed alternatives...