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Fractal Dimension and Efficient Markets
Máková, Barbora ; Krištoufek, Ladislav (advisor) ; Víšek, Jan Ámos (referee)
The efficient market hypothesis is one of the most important propositions in finance theory and has been subjected to years of rigorous empirical testing. We examine power of a new tool for evaluating market efficiency, fractal dimension. Characteristics and abilities of fractal dimension measure are explored through extensive Monte Carlo simulations. We prove that it provides an accurate evaluation of market's efficiency and its changes. This approach is highly innovative and creates new possibilities for examination of markets. The uniqueness of fractal dimension is in its ability to assign a numerical ranking to examined series describing the level of (in)efficiency; it is accurate for small samples of observations and quickly reflects changes in market efficiency structure. Powered by TCPDF (www.tcpdf.org)
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Fractal dimension and its estimation
Jajcay, Nikola ; Raidl, Aleš (advisor) ; Mikšovský, Jiří (referee)
This bachelor's thesis topic is fractal dimension and its estimations. First chapter is dedicated to brief history of fractal geometry and its basic ideas. In second chapter I was developing basic ideas of deterministic chaos and its applications on two different dynamic systems: logistic map and Lorenz's model of convection in atmosphere. Third chapter is dedicated to quantifiers of chaos, such as dynamic quantifiers, Lyapunov exponents and entropy, and geometric quantifiers, which means several fractal dimensions. I defined different types of fractal dimensions, their differencies and its advatages and disadvantages in many ways: geometric and numerical estimations. Fourth chapter is devoted to implementations of correlation algorithm to numerical estimation and it use to estimate correlation dimension of Lorenz's and Hénon's atractor. In the end of this thesis I recapitulated the results and compared it to results of other authors.
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Hausdirff metric and its application in fractals
Roháľ, Branislav Ján ; Hušek, Miroslav (advisor) ; Pyrih, Pavel (referee)
Title: Hausdorff metric and its application in fractals Author: Branislav Ján Roháľ Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Miroslav Hušek, DrSc., Department of Mathematical Analysis Abstract: In this thesis we focus on the themes naturally connected with the con- cept of a fractal. In the first part of the thesis we pay attention to Banach fixed point theorem and to the Hausdorff metric which are later used when studying self-similar sets. There are included parts on the Hausdorff, similarity, and box- counting dimension, too. In the second part of the thesis the new approaches to fractal dimension and some their properties are refered. We introduce generaliza- tion of this concept for any space admitting a fractal structure and for a distance space where also the "size" of sets on each level of fractal structure is considered. In the last chapter the contribution of new approache is demonstrated, - this enables defining the notion needed and counting fractal dimension where it was not possible under the classical approaches, too. Application to the domain of words and counting of dimensions of a language generated by a regular expresion are presented. Keywords: Hausdorff metric, Banach fixed point theorem, self-similar set, Hausdorff dimension, fractal dimension
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Characterisation of the Physical Chemical Processes Using the Fractal and Harmonic Analysis
Haderka, Jan ; Nešpůrek, Stanislav (referee) ; Mikula,, Milan (referee) ; Zmeškal, Oldřich (advisor)
Existuje mnoho různých způsobů jak analyzovat disperzní systémy a fyzikálně chemické processy ke kterým v takových systémech dochází. Tato práce byla zaměřena na charakterizaci těchto procesů pomocí metod harmonické fraktální analýzy. Obrazová data sledovaných systémů byly analyzovány pomocí waveletové analýzy. V průběhu práce byly navrženy různé optimalizace samotné analýzy, převážně zaměřené na odstranění manuálních operací během analýzy a tyto optimalizace byly také inkorporovány do softérového vybavení pro Harmonickou Fraktální Analýzu HarFA, který je vyvíjen na Fakultě chemické, VUT Brno.
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Capital Asset Price Modelling: Concept VAPM
Kuklik, Robert G. ; Janda, Karel (advisor) ; Kodera, Jan (referee) ; Lukáš, Ladislav (referee)
The key objective of this thesis is the outline of an alternative capital market modeling framework, the Volatility Asset Pricing Model, VAPM, inspired by the innovative dual approach of Mandelbrot and Hudson using the method based on synthesis of two seemingly antagonistic factors -- the volatility of market prices and their serial dependence determining the capital markets' dynamics. The pilot tests of this model in various periods using the market index as well as a portfolio of selected securities delivered generally satisfactory results. Firstly, the work delivers a brief recapitulation regarding the concepts of a consumer/investor choice under general conditions of hypothetical certainty. Secondly, this outline is then followed by a description of the "classical" methodologies in the risky environment of uncertainty, with assessment of their corresponding key models, i.e. the CAPM, SIM, MIM, APTM, etc., notwithstanding results of the related testing approaches. Thirdly, this assessment is based on evaluation of the underlying doctrine of Efficient Market Hypothesis in relation to the so called Random Walk Model. Fourthly, in this context the work also offers a brief exposure to a few selected tests of these contraversial concepts. Fifthly, the main points of conteporary approaches such as the Fractal Dimension and the Hurst Exponent in the dynamic framework of information entropy are subsequently described as the theoretical tools leading to development of the abovementioned model VAPM. The major contribution of this thesis is considered its attempt to apply the abovementioned concepts in practice, with the intention to possibly inspire a further analytical research.
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Fractural based microstructural damane evaluation in Ni-based superalloy gas turbine blades
Tarafder, M. ; Dlouhý, Ivo ; Hore, S. ; Das, S. K.
A fractal based evaluation of microstructural damage in Ni based superalloy cast IN 738 LC used in gas turbine blades is presented in the paper. Non-destructive in-situ replica method was used without damaging the blades for the evaluation of microstructure. The theoretical life of the stator blades of the gas turbine, which was exposed to temperature varying between 1060°C to 1100°C, was approximately 100,000 hours. In order to assess the suitability of the stator blades after 50% of the service life, fractal based microstructural damage evaluation has been conducted. The fractal dimensions of the in situ metallographic images can be correlated to the progressive deterioration of hardness at various locations of the blades. The extent of damage is inversely proportional to the fractal dimension. For fractal dimension below 2.4, the material can be classified as substantially damaged.
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Fraktální anisotropie a heterogenita lomových ploch oceli
Strnadel, B. ; Dlouhý, Ivo
The change in the fractal dimension of the fracture surface demonstrates a wavy character and dispersion depending on the microstructural state of the tested steel. The results of the fractal analysis in the crack growth direction and across the entire crack front were used as the basis for a reconstruction of the geometry of the fracture surface. The competing effects of transgranular and intergranular brittle fracture may lead to increased roughness of the fracture surface and its fractal dimension.
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