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Modeling of Long Memory in Volatility Using Wavelets
Kraicová, Lucie ; Baruník, Jozef (advisor) ; Adam, Tomáš (referee)
ii Abstract This thesis focuses on one of the attractive topics of current financial literature, the application of wavelet-based methods in volatility modeling. It introduces a new, wavelet-based estimator (wavelet Whittle estimator) of a FIEGARCH model, ARCH- family model capturing long-memory and asymmetry in volatility, and studies its properties. Based on an extensive Monte Carlo experiment, both the behavior of the new estimator in various situations and its relative performance with respect to two more traditional estimators (maximum likelihood estimator and Fourier-based Whittle estimator) are assessed, along with practical aspects of its application. Possible solutions are proposed for most of the issues detected, including suggestion of a new specification of the estimator. This uses maximal overlap discrete wavelet transform instead of the traditionally used discrete wavelet transform, which should improve the estimator performance in all its applications, not only in the case of FIEGARCH model estimation. The thesis concludes that, after optimization of the estimation setup, the wavelet-based estimator may become an attractive robust alternative to the traditional methods.
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Investment horizon in the CAPM: A comparison of a wavelet-based decomposition and the fractal regression
Spousta, Radek ; Krištoufek, Ladislav (advisor) ; Vácha, Lukáš (referee)
This thesis study two promising methods used to define the multiscale CAPM - the wavelet-based decomposition and the fractal regression. Their estimates, obtained on monthly excess return on ten portfolios formed on beta in the US market, are compared in the period from November 2000 to October 2020 and, subsequently, in the period from November 1965 to October 2020. In the first period, the multiscale beta is not significantly different from the original single-scale beta for most of the portfolios. Contrary, both methods uncover significant multiscale behavior of the beta in the second period. Specifically, the high-beta portfolios have higher multiscale beta at longer investment horizons, mainly at wavelet scale 3 and scales 12-24 of the fractal regression. Overall, both methods deliver consistent results, and seem suitable for extending the CAPM with an investment horizon. JEL Classification Keywords G12, C20 CAPM, asset pricing, multiscale analysis, wavelets, fractal regression Title Investment horizon in the CAPM: A comparison of a wavelet-based decomposition and the fractal regression
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Collagen structures from cell culture to intact tendon
Hadraba, Daniel ; Jelen, Karel (advisor) ; Amler, Evžen (referee) ; Plášek, Jaromír (referee)
CHARLES UNIVERSITY and HASSELT UNIVERSITY / tUL Doctoral dissertation Collagen structures from cell culture to intact tendon ABSTRACT Author: Daniel Hadraba Promoters: Assoc. Prof. Karel Jelen | Charles University Prof. Marcel Ameloot | Hasselt University Co-promoters: Dr. Frantisek Lopot | Charles University Prof. Virginie Bito | Hasselt University Annotation Author: Ing. Mgr. Daniel Hadraba Doctoral thesis title: Collagen structures from cell culture to intact tendon Year: 2010 - 2017 Doctoral program: Doctor of Biomechanics at Charles University Doctor of Biomedical Science at Hasselt University / transnational University Limburg Departments: Dept. Anatomy and Biomechanics | Faculty of Physical Education and Sport | Charles University Dept. Biophysics | Hasselt University Promoters: Assoc. Prof. Karel Jelen | Dept. Anatomy and Biomechanics | Faculty of Physical Education and Sport | Charles University Prof. Marcel Ameloot | Hasselt University / transnational University Limburg Co-promoters: Dr. Frantisek Lopot | Dept. Anatomy and Biomechanics | Faculty of Physical Education and Sport | Charles University Prof. Virginie Bito | Hasselt University / transnational University Limburg Bibliography details: Pages 102 Figures 30 Tables 2 Equations 17 Keywords: tendon, collagen, crimps, orientation, aging,...
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Fama-French Model: Multiscale Portfolio Analysis
Spousta, Radek ; Kraicová, Lucie (advisor) ; Teplý, Petr (referee)
This thesis studies the empirical relationship between excess asset returns and the Fama−French risk factors at various scales using a combination of the Fama−French model and wavelet-based methods. We re-examine previously published results obtained for six portfolios formed on size and book-to-market ratio in the U.S. market, and focus on the influence of different scales on the original results. We conclude that the most the total variance of the risk factors and excess portfolio returns is concentrated at scale 1 and 2, which corresponds to periodicities of 2-4 months and 4-8 months, respectively. Next, we observe significant variation in estimated parameters across different scales. Furthermore, some of the Fama−French risk factors are strongly correlated at scale 2, 3 and 4, which is unobservable in standard correlation matrix. Overall, the multiscale approach seems beneficial for analysis of the Fama−French three-factor model as it reveals information that remains hidden to traditional methods.
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Collagen structures from cell culture to intact tendon
Hadraba, Daniel ; Jelen, Karel (advisor) ; Amler, Evžen (referee) ; Plášek, Jaromír (referee)
CHARLES UNIVERSITY and HASSELT UNIVERSITY / tUL Doctoral dissertation Collagen structures from cell culture to intact tendon ABSTRACT Author: Daniel Hadraba Promoters: Assoc. Prof. Karel Jelen | Charles University Prof. Marcel Ameloot | Hasselt University Co-promoters: Dr. Frantisek Lopot | Charles University Prof. Virginie Bito | Hasselt University Annotation Author: Ing. Mgr. Daniel Hadraba Doctoral thesis title: Collagen structures from cell culture to intact tendon Year: 2010 - 2017 Doctoral program: Doctor of Biomechanics at Charles University Doctor of Biomedical Science at Hasselt University / transnational University Limburg Departments: Dept. Anatomy and Biomechanics | Faculty of Physical Education and Sport | Charles University Dept. Biophysics | Hasselt University Promoters: Assoc. Prof. Karel Jelen | Dept. Anatomy and Biomechanics | Faculty of Physical Education and Sport | Charles University Prof. Marcel Ameloot | Hasselt University / transnational University Limburg Co-promoters: Dr. Frantisek Lopot | Dept. Anatomy and Biomechanics | Faculty of Physical Education and Sport | Charles University Prof. Virginie Bito | Hasselt University / transnational University Limburg Bibliography details: Pages 102 Figures 30 Tables 2 Equations 17 Keywords: tendon, collagen, crimps, orientation, aging,...
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Application of band spectrum regression in economic problems
Zubaľ, Andrej ; Baruník, Jozef (advisor) ; Víšek, Jan Ámos (referee)
In recent years, there has been a rise of interest in the use of various spectral methods in economics and econometrics. These methods have their theoretical background in mathematics, particularly in Fourier analysis. The less tradi- tional and relatively new branch of methods stems from the so-called wavelet analysis. Wavelet methods are believed to have a wide applicability in the anal- ysis of economic time series. The motivation for this thesis is to introduce these methods and apply them in the analysis of economic problems, thereby showing their usefulness within the economic context. Particular attention is paid to band spectrum regression, which allows for decomposition of economic relation- ships into different frequency components. In this work, we use wavelet band spectrum regression, among other wavelet methods, to analyze the relation- ship between realized and implied volatilities for the price of crude oil. Second application is from the field of macroeconomics. We analyze the relationship between unemployment and labor productivity growth for four major European economies. 1
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Modeling of Long Memory in Volatility Using Wavelets
Kraicová, Lucie ; Baruník, Jozef (advisor) ; Adam, Tomáš (referee)
ii Abstract This thesis focuses on one of the attractive topics of current financial literature, the application of wavelet-based methods in volatility modeling. It introduces a new, wavelet-based estimator (wavelet Whittle estimator) of a FIEGARCH model, ARCH- family model capturing long-memory and asymmetry in volatility, and studies its properties. Based on an extensive Monte Carlo experiment, both the behavior of the new estimator in various situations and its relative performance with respect to two more traditional estimators (maximum likelihood estimator and Fourier-based Whittle estimator) are assessed, along with practical aspects of its application. Possible solutions are proposed for most of the issues detected, including suggestion of a new specification of the estimator. This uses maximal overlap discrete wavelet transform instead of the traditionally used discrete wavelet transform, which should improve the estimator performance in all its applications, not only in the case of FIEGARCH model estimation. The thesis concludes that, after optimization of the estimation setup, the wavelet-based estimator may become an attractive robust alternative to the traditional methods.
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Detection and Tracking of Small Moving Objects
Filip, Jan ; Zuzaňák, Jiří (referee) ; Hradiš, Michal (advisor)
Thesis deals with the detection and tracking of small moving objects from static images. This work shows a general overview of methods and approaches to detection and tracking of objects. There are also described some other approaches to the whole solution. It also included basic definitions, such a noise, convolution and mathematical morphology. The work described Bayesian filtering and Kalman filter. It described the theory of Wavelets, wavelets filters and transformations. The work deals with different ways of the blob`s detection. It is here the design and implementation of applications, which is based on the wavelets filters and Kalman filter. It`s implemented several methods of background subtraction, which are compared by testing. Testing and application are designed to detect vehicles, which are moving faraway (at least 200 m away).
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