Anhand von Temperaturdaten des Standortes Berlin-Tegel wird der Temperaturverlauf für einen Zeitraum von 15 Jahren modelliert. Es werden zwei verschiedene Regressionsansätze gegenübergestellt. Zuerst werden die Daten anhand einer Zeitreihenanalyse geschätzt. Dieses parametrische Verfahren wird mit der nicht-parametrischen Methode des Shape Invariant Modeling verglichen. Beiden Ansätzen liegt die Methode der Kleinsten Fehlerquadrate zugrunde. Die Zeitreihenanalyse als Spezialgebiet der Regressionsanalyse wird mit Hilfe einer Fourierreihe realisiert, um den periodischen Verlauf der Funktion abbilden zu können. Beim Shape Invariant Model werden mithilfe einer Referenzkurve die individuellen Regressionsfunktionen ermittelt. Als Referenz dient ein Basistag. Die Parameterschätzer werden durch Achsentransformation ermittelt.

This thesis examines three decomposition techniques and their usability for economic and financial time series. The stock index DAX30 and the exchange rate from British pound to US dollar are used as representative economic time series. Additionally, autoregressive and conditional heteroscedastic simulations are analysed as benchmark processes to the real data. Discrete wavelet transform (DWT) uses wavelike functions to adapt the behaviour of time series on different time scales. The second method is the singular spectral analysis (SSA), which is applied to extract influential reconstructed modes. As a third algorithm, empirical mode decomposition (END) leads to intrinsic mode functions, who reflect the short and long term fluctuations of the time series. Some problems arise in the decomposition process, such as bleeding at the DWT method or mode mixing of multiple EMD mode functions. Conclusions to evaluate the predictability of the time series are drawn based on entropy - and recurrence - analysis. The cyclic behaviour of the decompositions is examined via the coefficient of variation, based on the instantaneous frequency. The results show rising predictability, especially on higher decomposition levels. The instantaneous frequency measure leads to low values for regular oscillatory cycles, irregular behaviour results in a high variation coefficient. The singular spectral analysis show frequency - stable cycles in the reconstructed modes, but represents the influences of the original time series worse than the other two methods, which show on the contrary very little frequency - stability in the extracted details.