A class of semiparametric fractional autoregressive GARCH models (SEMIFARGARCH), which includes deterministic trends, difference stationarity and stationarity with short- and long-range dependence, and heteroskedastic model errors, is very powerful for modelling financial time series. This paper...

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),...

The distinction between stationarity, difference stationarity, deterministic trends as well as between short- and long-range dependence has a major impact on statistical conclusions, such as confidence intervals for population quantities or point and interval forecasts. In this paper, recent...

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...

We consider dependence structures in multivariate time series that are characterized by deterministic trends. Results from spectral analysis for stationary processes are extended to deterministic trend functions. A regression cross covariance and spectrum are defined. Estimation of these...

Time series in many areas of application often display local or global trends. Typical models that provide statistical "explanations" of such trends are, for example, polynomial regression, smooth bounded trends that are estimated nonparametrically, and difference-stationary processes such as,...

Filtered log-periodogram regression estimation of the fractional differencing parameter d is considered. Asymptotic properties are derived and the effect of filtering on ˆ d is investigated. It is shown that the estimator by Geweke and Porter-Hudak (1983) can be improved significantly using a...

We consider temporal aggregation of stationary and nonstationary time series with short memory, long memory and antipersistence, within the framework of fractional autoregressive processes. Asymptotically, long memory and antipersistence are preserved whereas short memory components vanish. In...

In this paper data-driven algorithms for fitting SEMIFAR models (Beran, 1999) are proposed. The algorithms combine the data-driven estimation of the nonparametric trend and maximum likelihood estimation of the parameters. For selecting the bandwidth, the proposal of Beran and Feng (1999) based...