The contents of this dissertation are on a semiparametric extension of the ACD model of Engle and Russell (1998). The proposal of the Semi-ACD model is based on the decomposition of the data of interest into a deterministic and a stochastic part, whereby the former is assumed to be time-varying. A non-negative, time-varying, smooth scale function is included into the model to take this into account, which is estimated with a local polynomial regression An automatic iterative plug-in bandwidth selection algorithm is developed. A simulation study evaluates the Semi-ACD model on the basis of various criteria. An extension of the proposal to log data shows that the estimation of the scale function is clearly simplified. In addition, decisive theoretical properties for the Semi-Log-ACD model are derived and the bandwidth selection algorithm is further automated. To forecast non-negative financial data, the above models are combined with known and new forecasting methods. In order to not limit the flexibility of the semiparametric idea, bootstrap methods are chosen as nonparametric forecasting methods. Compared to model-based Kalman filter predictions, these give not the best forecasts, but are clearly better compared to the corresponding parametric model forecasts. The algorithm is further applied to forecast the log-GDP of developing and developed countries. Random Walk models with a constant drift, a linear drift and a local linear drift are applied, as well. It is found that combining forecasting methods improves the forecasts and especially including the local linear regression method stabilizes the forecasts and enables the detection of variations in the trend process, that are typical for developing countries. Promising research questions to further improve the Semi-(Log-)ACD models are presented.