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...

Estimation of a nonparametric regression spectrum based on the periodogram is considered. Neither trend estimation nor smoothing of the periodogram are required. Alternatively, for cases where spectral estimation of phase shifts fails and the shift does not depend on frequency, a time domain...

A class of semiparametric fractional autoregressive GARCH models (SEMIFAR-GARCH), 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...

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

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...

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...