In this paper we propose using a nonparametric model specification test for parametric time series with long-range dependence (LRD). In order to establish asymptotic distributions of the proposed test statistic, we develop new central limit theorems for certain weighted quadratic forms of...

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.

A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities...

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 dependent. An asymptotically normal test is established even when long-range dependent is involved. To implement the proposed...

Let Xt be a moving average process defined by Xt=[summation operator]k=0[infinity][psi]k[var epsilon]t-k, t=1,2,... , where the innovation {[var epsilon]k} is a centered sequence of random variables and {[psi]k} is a sequence of real numbers. Under conditions on {[psi]k} which entail that {Xt}...