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.
Inhaltsverzeichnis (Table of Contents)
- Introduction
- Theoretical Background
- Frequency Domain
- Discrete Fourier Transform (DFT) and Inverse Discrete Fourier Transform (IDFT)
- Filters in the Frequency Domain
- Convolution theorem and transfer function
- Amplitude, Phase and Time-Shift Functions
- Symmetric Filters
- Low-Pass Filter
- High-Pass Filter
- Band-Pass Filter
- Advanced Filters
- MA(q)-Filter
- AR(p)-Filter.
- ARMA(p,q)-Filter
- Direct Filter Approach (DFA)
- Optimization Criterion: MMSFE
- Decomposition of the MMSFE
- Real-time detection of turning points using DFA
- Improving Speed
- Reconciling Speed and Reliability
- Level and Time Delay Constraints
- Performance Measurement
- Drawdown and Maximum Drawdown
- R-squared .
- Sharpe Ratio
- Return on Investment.
- Experiment Design and Empirical Results
- A Brief Analysis of the S&P 500 Index
- Frequential Analysis
- Log-returns.
- Filter selection based on the Periodogram
- Application of the Direct Filter Approach (DFA)
- In-sample Analysis.
- Coefficient estimation
- Out-of-sample Analysis
- Methods
- In-sample Analysis.
- Turning Points Identification
- Method Description
- Analysis
- A Brief Analysis of the CBOE Volatility Index (VIX)
- Coefficient Estimation
- VIX as strategic extension for the S&P
- Frequential Analysis
- A Brief Analysis of the EURO STOXX 50 Index
- Analysis .
- A Brief Analysis of the EURO STOXX 50 Volatility Index (VSTOXX)
- Analysis
- VSTOXX as strategic extension for the EURO STOXX
- Strategy Development
- Modeling enhancement
- A Brief Analysis of the exchange rate (EURO/US-$)
- Analysis
- Relationship and link between S&P and EURO STOXX
- A Brief Analysis of the exchange rate (EURO/US-$)
- Final Results
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This thesis aims to evaluate and compare different variants of the DFA procedure to find a method for the effective identification of turning points in important financial time series. It further explores the development of suitable investment strategies based on these results.- Real-time identification of turning points in financial time series
- Evaluation and comparison of different DFA variants
- Development of investment strategies based on DFA results
- Analysis of S&P 500, EURO STOXX 50, and their implied volatility indices
- Application of frequential analysis and DFA techniques
Zusammenfassung der Kapitel (Chapter Summaries)
- Introduction: Introduces the context of the thesis, highlighting the growing need for accurate and early identification of turning points in financial time series. It emphasizes the importance of DFA methodology for addressing this need.
- Theoretical Background: Provides a comprehensive overview of relevant theoretical concepts. This includes frequency domain analysis, the Discrete Fourier Transform (DFT), filters in the frequency domain, and a detailed explanation of the Direct Filter Approach (DFA) methodology. It covers various optimization criteria, real-time detection of turning points, and performance measurement techniques like drawdown, R-squared, and Sharpe Ratio.
- Experiment Design and Empirical Results: This chapter outlines the design and implementation of the empirical study. It delves into the analysis of the S&P 500 Index, focusing on frequential analysis, the application of DFA, and the identification of turning points. This chapter also includes the analysis of the CBOE Volatility Index (VIX) and its potential as a strategic extension for the S&P 500. The chapter then transitions to a similar analysis of the EURO STOXX 50 Index and its volatility index (VSTOXX), exploring their relationship and the potential for strategic extension.
- Strategy Development: This chapter outlines the development of various investment strategies based on the results obtained from the DFA analysis. It explores different strategies and their implications for profit optimization.
- Modeling enhancement: This chapter examines the modeling enhancements by analyzing the exchange rate (EURO/US-$) and its relationship to the S&P and EURO STOXX indices. This analysis aims to understand the cyclical and structural influence of the exchange rate and its potential for further refining the model.
Schlüsselwörter (Keywords)
The primary focus of this thesis is on the Direct Filter Approach (DFA) and its application to real-time financial time series analysis. This work explores turning point identification, algorithmic trading, and investment strategies. Key financial indices analyzed include S&P 500, EURO STOXX 50, and their corresponding volatility indices (VIX and VSTOXX). The study also investigates the role of exchange rate dynamics in refining the DFA model. Further key concepts include frequential analysis, Fourier transforms, and performance metrics like R-squared and Sharpe Ratio. - A Brief Analysis of the S&P 500 Index
- Frequency Domain
- Quote paper
- Ueli Hartmann (Author), Felipe Ramirez (Author), 2012, Real Time Detection of Turning Points in Financial Time Series, Munich, GRIN Verlag, https://www.grin.com/document/211451
