Let be a family of (N,d)-anisotropic Gaussian random fields with generalized Hurst indices H=(H1,...,HN)[set membership, variant](0,1)N. Under certain general conditions, we prove that the local time of is jointly continuous whenever . Moreover we show that, when H approaches H0, the law of the...

Let be the solution process for the following Cauchy problem for the stochastic fractional partial differential equation taking values in : where (1[alpha]3, [delta]=min{[alpha]-[[alpha]],2+[[alpha]]2-[alpha]}) is the fractional differential operator with respect to the spatial variable x (see...

This paper studies a nonlinear cointegrating regression model with nonlinear nonstationary heteroskedastic error processes. We establish uniform consistency for the conventional kernel estimate of the unknown regression function and develop atwo-stage approach for the estimation of the...

In this paper we investigate the weighted bootstrap for U-statistics and its properties. Under very general choices of random weights and certain regularity conditions, we show that the weighted bootstrap method with U-statistics provides second-order accurate approximations to the distribution...

We examine a kernel regression smoother for time series that takes account of the error correlation structure as proposed by Xiao et al. (2008). We show that this method continues to improve estimation in the case where the regressor is a unit root or near unit root process.

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is...

This paper proposes a model specification testing procedure for parametric specification of the conditional mean function in a nonlinear time series model with long–range dependence. An asymptotically normal test is established even when long–range dependence is involved. In order to...

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary...

In this note, we discuss the Kolmogrov and Erdös test for self-normalized sums. Some general results are obtained.

In this paper, we obtain the optimal rate of convergence in the central limit theorem for m-dependent U-statistics under mild conditions, which is similar to that in the independent rv's.