The importance of wind speed predictions, which is the source for wind power, is in the focus of interest. Accurate predictions are crucial for the energy production. Developing short-term wind forecasts helps to increase the productivity of wind energy. Moreover, the energy supply can be optimized, by increasing the accuracy of wind speed predictions, particularly the feed-in of wind power. The wind speed forecasting approaches presented here use 10-minute data collected at several stations in Germany. An overview of different periodic and seasonal time series models are given. The seasonality that is modelled by some periodic base function is combined with a long memory process and heteroscedasticity. Therefore, an ARFIMA(p,d,q)-APARCH(P,Q) process is comprised and applied to the correlated residuals. In contrast to the classical Fourier functions, cubic B-splines are used to model the periodicity. Furthermore, a common time series model is provided and applied to the wind speed. The feature is a time-saving approach for modelling and predicting. Hence, we introduce an iteratively reweighted least squares and lasso method. The most important findings are forecasting enhancements up to six hours and a simple and fast estimation and prediction method