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...

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...

SEMIFAR models introduced in Beran (1999) provide a semiparametric modelling framework that enables the data analyst to separate deterministic and stochastic trends as well as short- and long-memory components in an observed time series. A correct distinction between these components, and in...

We consider parameter estimation for time-dependent locally stationary long-memory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and 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...

The problem of predicting 0-1-events is considered under general conditions, including stationary processes with short and long memory as well as processes with changing distribution patterns. Nonparametric estimates of the probability function and prediction intervals are obtained.