By applying SEMIFAR models, we examine "long memory" in the volatility of worldwide stock-market indexes. Our analysis yields strong evidence of "long memory" in stock-market volatility, either in terms of stochastic long-range dependence or in the form of deterministic trends. In some cases,...

Duration series often exhibit long-range dependence and local nonstationarities. Here, exponential FARIMA (EFARIMA) and exponential SEMIFAR (ESEMIFAR) models are introduced. These models capture simultaneously nonstationarities in the mean as well as short- and long-range dependence, while...

A new approach to tail index estimation based on huberization of the Pareto MLE is considered. The proposed estimator is robust in a nonstandard way in that it protects against deviations from the central model at low quantiles. Asymptotic normality with the parametric n-rate of convergence is...

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...

Recent results on so-called SEMIFAR models introduced by Beran (1997) are discussed. The nonparametric deterministic trend is estimated by a kernel method. The differencing and fractional differencing parameters as well as the autoregressive coefficients are estimated by an approximate maximum...

Asymptotic properties of the harmonic moment tail index Estimator are derived for distributions with regularly varying tails. The estimator shows good robustness properties and stands out for its simplicity. A tuning parameter allows for regulating the trade-off between robustness and...