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Most major airports collect recordings of the position of aircrafts at specific times. Those data typically requires extensive smoothing and corrections before it can be used for later analysis. Conventional smoothing approaches fail to model the movement physically correct, i.e. do not take standstills of aircrafts into account.
In this thesis we develop a method to detect standstills, employ robust smoothing splines for data fitting, add adequate boundary conditions for the detected standstill periods (i.e. force the function to be constant and to entry- and exit-direction for the standstills to be identical) and give an algorithm to solve those approximation problems efficiently.
In the progress we give an explicit proof for the convergence of the IRLS algorithm proposed by Huber to solve M-type estimates for non-linear approximation problems. Furthermore we derive a blueprint for a method to solve separable, quadratic least squares problems with very few quadratic variables.
Prediction of economic variables is a basic component not only for economic models, but also for many business decisions. Nevertheless it is difficult to produce accurate predictions in times of economic crises, which cause nonlinear effects in the data. In this dissertation a nonlinear model for analysis of time series with nonlinear effects is introduced. Linear autoregressive processes are extended by neural networks to overcome the problem of nonlinearity. This idea is based on the universal approximation property of single hidden layer feedforward neural networks of Hornik (1993). Univariate Autoregressive Neural Network Processes (AR-NN) as well as Vector Autoregressive Neural Network Processes (VAR-NN) and Neural Network Vector Error Correction Models (NN-VEC) are introduced. Various methods for variable selection, parameter estimation and inference are discussed. AR-NN's as well as a NN-VEC are used for prediction and analysis of the relationships between 4 variables related to the German automobile industry: The US Dollar to Euro exchange rate, the industrial output of the German automobile industry, the sales of imported cars in the USA and an index of shares of German automobile manufacturing companies. Prediction results are compared to various linear and nonlinear univariate and multivariate models.