Prediction in time series models with a trend requires reliable estima- tion 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...

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...

Nonparametric regression with long-range and antipersistent errors is considered. Local polynomial smoothing is investigated for the estimation of the trend function and its derivatives. It is well known that in the presence of long memory (with a fractional differencing parameter 0 d 1/2),...

This paper summarizes recent developments in non- and semiparametric regres- sion with stationary fractional time series errors, where the error process may be short-range, long-range dependent or antipersistent. The trend function in this model is estimated nonparametrically, while the...

This paper considers estimation of the regression function and its derivatives in nonparametric regression with fractional time series errors. We focus on investigating the properties of a kernel dependent function V (delta) in the asymptotic variance and finding closed form formula of it, where...