Research Paper (undergraduate) from the year 2012 in the subject Mathematics - Applied Mathematics, grade: 5.5, ZHAW Zurcher Hochschule fur Angewandte Wissenschaften, language: English, abstract: As a consequence of the recent financial crisis, institutions are increasingly interested in identifying turning points in financial time series. The accurate and early identification of these turning points can result in the optimal exploitation of the invested capital and profit maximization. Most existing methods for the real-time identification of turning points have proved unreliable and therefore the need to develop a cutting-edge model. The DFA methodology of Prof. Dr. Marc Wildi is one promising real-time procedure that seeks to solve this problem. The purpose of this thesis is the evaluation and comparison of different variants of the DFA procedure in order to find a method for the effective identification of turning points in important financial time series, such as the S\&P 500 and the EUROSTOXX 50 and their implied volatility indices (VIX and VSTOXX, resp.). Further, this thesis aims to develop a suitable investment strategy based on the obtained results. For the purpose of this thesis, the time series mentioned above were analyzed between the years 1990 and 2011, using the last year as out-of-sample data. Frequential analysis using Fourier transforms as well as different variants of the DFA-algorithm were applied in order to identify the desired turning points. The results obtained from these analyses of the S\&P 500 and EUROSTOXX 50 time series show a considerable out-of-sample investment return which verifies the validity of the model. On a second level of analysis, using the implied volatility indices it was possible to generalize the model and thereby verify the initial results. Moreover, with the help of the development of further investment strategies it was possible to normalize profit returns, maintaining a semi-constant growth, which is usually preferred by financial institutions. Finally, given the structural similarities of the two main financial series examined, whose clear profile was only observable using the DFA system, it was possible to combine both time series using the daily exchange rate as a cyclical and structural catalyst, thus achieving a deeper thrust of the model. This all was possible by highlighting the flexibility of the DFA model for real-time analysis of financial time series and its practical application as a tool for investment analysis. Therefore, the DFA Modell enables an accurate real-time identification of tuning points in financial series.
