A flexible class of anisotropic stationary lattice processes with long memory can be defined in terms of a two-way fractional ARIMA (FARIMA) representation. We consider parameter estimation based on minimizing an approximate residual sum of squares. The method can be applied to sampling areas...

A class of circular processes based on Gaussian subordination is introduced. This allows for flexible modelling of directional time series with long-range dependence. Based on limit theorems for subordinated processes and consistent estimation of nuisance parameters, asymptotic confidence...

We investigate the behavior of nonparametric kernel M-estimators in the presence of long-memory errors. The optimal bandwidth and a central limit theorem are obtained. It turns out that in the Gaussian case all kernel M-estimators have the same limiting normal distribution. The motivation behind...

Prediction in time series models with a trend requires reliable estimation of the trend function at the right end of the observed series. Local polynomial smoothing is a suitable tool because boundary corrections are included implicitly. However, outliers may lead to unreliable estimates, if...