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Clouds and Hills Generation Using Fractal Geometry
Tůma, Petr ; Zuzaňák, Jiří (referee) ; Venera, Jiří (advisor)
This work is concerned with generation of landscape objects using fractal geometry. In this work is explained what the fractal is and terms associated with them. The other parts describe basic theoretical ideas and implementation of these algorithms. The Capital theme is generation of models clouds and hills in values of input parameters, their presentation and date media saved there. The project includes my algorithm extension for hills generation of course. At the conclusion of this work are summarized tendencies of next development and my results.
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Analysis and Prediction of Foreign Exchange Markets by Chaotic Attractors and Neural Networks
Pekárek, Jan ; Dostál, Petr (referee) ; Budík, Jan (advisor)
This thesis deals with a complex analysis and prediction of foreign exchange markets. It uses advanced artificial intelligence methods, namely neural networks and chaos theory. It introduces unconventional approaches and methods of each of these areas, compares them and uses on a real problem. The core of this thesis is a comparison of several prediction models based on completely different principles and underlying theories. The outcome is then a selection of the most appropriate prediction model called NAR + H. The model is evaluated according to several criteria, the pros and cons are discussed and approximate expected profitability and risk are calculated. All analytical, prediction and partial algorithms are implemented in Matlab development environment and form a unified library of all used functions and scripts. It also may be considered as a secondary main outcome of the thesis.
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The Use of Artificial Intelligence on Stock Market
Barjak, Maroš ; Budík, Jan (referee) ; Dostál, Petr (advisor)
The thesis deals with design, implementation and optimization of a model based on artificial intelligence and neural networks, which is able to predict future time series prices on a stock market. Main goal is to create an object oriented application for successful future trend prediction of financial derivatives with the use of cooperating methods such as Hurst exponent evaluation and automated market simulation.
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On multifractality and predictability of financial time series
Heller, Michael ; Krištoufek, Ladislav (advisor) ; Vácha, Lukáš (referee)
The aim of this thesis is to examine an empirical relationship between multifrac- tality of financial time series and its returns. We approach the multifractality of a given time series as a measure of its complexity. Multifractal financial time series exhibit repeating self-similar patterns. Multifractality could be a good predictor of stock returns or a factor which can be used in asset pricing. We expected that capturing the complexity of a given time series by a model, a positive or a negative risk premia for investing into "more multifractal assets" could be found. Daily prices of 31 stock indices and daily returns of 10-years US government bonds were downloaded. All the data were recorded between 2012 and 2021. After estimation the multifractal spectra, applying MF-DFA method, of all stock indices, we ordered all stock indices from the lowest to the most multifractal. Then, we constructed a "multifractal portfolio" holding a long position in the 7 most multifractal and holding a short position in the 7 least multifractal stock indices. Fama-MacBeth regression with market risk premia and multifractal variable as independent variables was applied. Multi- fractality in all examined financial time series was found. We also found a very low negative risk premia for holding "a multifractal...
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Entropy as a Measure of Predictability in Financial Time Series
Nahodil, Vladimír ; Krištoufek, Ladislav (advisor) ; Wang, Yao (referee)
This work studies stock markets efficiency and predictability using the information-theoretic concepts of approximate entropy (ApEn) and sample entropy (SampEn) and compares them to the estimates of the Hurst exponent. This is assessed together with the property of distinguishing between developing and developed markets. Moreover, an investment strategy based on the value of the sample entropy is tested. ApEn shows very weak relationship with other measures and performs poorly as a measure of efficiency. SampEn and the Hurst exponent clearly confirm lower overall efficiency of developing markets. The sample entropy also forms quite strong downward linear relationship with hit-rates of forecasting models. ARMA shows highest hit-rates in periods with SampEn values around 1.6 - 1.7. This could be considered as an investment strategy with lower risk; however, also as one with potentially lower accumulated returns due to smaller investing windows.
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Are financial returns and volatility multifractal at all?
Sedlaříková, Jana ; Krištoufek, Ladislav (advisor) ; Kraicová, Lucie (referee)
Over the last decades, multifractality has become a downright stylized fact in financial markets. However, its presence has not been adequately statistically proved. The main aim of this thesis is to contribute to the discussion by an ex- tensive statistical analysis of the problem. We investigate returns and volatility of the collection of the four stock indices employing the three popular methods: the GHE, the MF-DFA, and the MF-DMA method. By comparing the results of the original series to those for simulated monofractal series, we conclude that stock market returns as well as volatility exhibit a multifractal nature. Additionally, in order to understand the origin of underlying multifractality, we study vari- ous surrogate series. We found that a fat-tailed distribution significantly affects multifractality. On the other, we were not able to confirm the impact of time correlations as the results strongly depend on the applied model. JEL Classification F12, G02, G10, C12, C22, C49, C58 Keywords econophysics, multifractality, financial markets, Hurst exponent Author's e-mail jana.sedlarikova@gmail.com Supervisor's e-mail kristoufek@ies-prague.org
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Backtesting of Different Scaling Rules for Value at Risk in the Basel Context
Klečka, Adam ; Krištoufek, Ladislav (advisor) ; Avdulaj, Krenar (referee)
1 Abstract There is a discrepancy between two important horizon for Value at Risk modelling in the Basel context. We take 10-day values for determining the regulatory capital but we consider 1-day models for backtesting. The main objective of this thesis is to examine the suitability of the currently used Square Root of Time rule for Value at Risk scaling. We compare its performance with the method utilizing Hurst exponent. Our analysis is performed for both the normal and stable distribution. We conclude that the normality assumption and the Square Root of Time rule prevail under the regulatory parameters. The results of the Hurst exponent method are not favourable under normality. On the other hand, the performance for the stable distribution is quite satisfactory under non-Basel parameters and the Hurst exponent complements this distribution very well. Therefore, the use of stable distribution and the Hurst exponent method is justified when dealing with complex non-linear instruments, during turbulent periods, or for general non-Basel setting. In general however, our results are strongly data-dependent and further evidence is needed for any conclusive implications. JEL Classification G21, G28, C58, G32, C14, G18 Keywords value at risk, backtesting, volatility scaling, Basel II, stable distribution, Hurst...
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Multifractal Analysis of Stock Market Prices
Čechová, Kristýna ; Krištoufek, Ladislav (advisor) ; Vošvrda, Miloslav (referee)
The aim of this thesis is to provide an empirical evidence of multifractality in financial time series and to discuss the relevance of this concept for the current financial theory. We have applied two methods, the Multifractal Detrended Fluctuation analysis and the Generalized Hurst exponent method, on components of the Dow Jones Industrial Average. We analyzed daily data of 30 companies traded on U.S. stock markets from 2002 to 2012. We present results supporting presence of multiscaling in open-close returns. Contrary to published literature, we were not able to find any significant multiscaling in volatility. Moreover based on our analysis, multiscaling is not present in standardized returns and as multifractality requires relatively complicated models, this is our most valuable result. 1
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