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Environment for Lifting
Kubový, Jan ; Pelikán, Josef (advisor) ; Yaghob, Jakub (referee)
The aim of the thesis is to create a library that will provide ease way to cre- ating and experimenting with computing networks. The concpet of computing netowork can be explained as algorithms whitch can be devided into small simple parts (nodes). From these nodes the computing netowork can be build. Examples of such computational units are cryptographic algorithms. Most important com- puting network are these where exist inverse operations. Especially lifting-based transformations are important. The main emphasis of this work is on the sim- plicity of creating new nodes follows by sipmle nodes connecting. Versatility is another important feature in working with this library. This library will be used to easily implement and experiment with the various computing networks.
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Wavelet portfolio optimization: Investment horizons, stability in time and rebalancing
Kvasnička, Tomáš ; Krištoufek, Ladislav (advisor) ; Kukačka, Jiří (referee)
The main objective of the thesis is to analyse impact of wavelet covariance estimation in the context of Markowitz mean-variance portfolio selection. We use a rolling window to apply maximum overlap discrete wavelet transform to daily returns of 28 companies from DJIA 30 index. In each step, we compute portfolio weights of global minimum variance portfolio and use those weights in the out-of- sample forecasts of portfolio returns. We let rebalancing period to vary in order to test influence of long-term and short-term traders. Moreover, we test impact of different wavelet filters including Haar, D4 and LA8. Results reveal that only portfolios based on the first scale wavelet covariance produce significantly higher returns than portfolios based on the whole sample covariance. The disadvantage of those portfolios is higher riskiness of returns represented by higher Value at Risk and Expected Shortfall, as well as higher instability of portfolio weights represented by shorter period that is required for portfolio weights to significantly differ. The impact of different wavelet filters is rather minor. The results suggest that all relevant information about the financial market is contained in the first wavelet scale and that the dynamics of this scale is more intense than the dynamics of the whole market.
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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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Does wavelet decomposition and neural networks help to improve predictability of realized volatility?
Křehlík, Tomáš ; Baruník, Jozef (advisor) ; Vošvrda, Miloslav (referee)
I perform comprehensive comparison of the standard realised volatility estimators including a novel wavelet time-frequency estimator (Barunik and Vacha 2012) on wide variety of assets: crude oil, gold and S&P 500. The wavelet estimator allows to decompose the realised volatility into several investment horizons which is hypothesised in the literature to bring more information about the volatility time series. Moreover, I propose artificial neural networks (ANN) as a tool for forecasting of the realised volatility. Multi-layer perceptron and recursive neural networks typologies are used in the estimation. I forecast cumulative realised volatility on 1 day, 5 days, 10 days and 20 days ahead horizons. The forecasts from neural networks are benchmarked to a standard autoregressive fractionally integrated moving averages (ARFIMA) model and a mundane model. I confirm favourable features of the novel wavelet realised volatility estimator on crude oil and gold, and reject them in case of S&P 500. Possible explanation is an absence of jumps in this asset and hence over-adjustment of data for jumps by the estimator. In forecasting, the ANN models outperform the ARFIMA in terms of information content about dynamic structure of the time series.
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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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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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Modeling multivariate volatility using wavelet-based realized covariance estimator
Baruník, Jozef ; Vácha, Lukáš
Abstract. Study of the covariation have become one of the most active and successful areas of research in the time series econometrics and economic forecasting during the recent decades. Our work brings complete theory for the realized covariation estimation generalizing current knowledge and bringing the estimation to the time-frequency domain for the first time. The results generalize the popular realized volatility framework by bringing the robustness to noise as well jumps and ability to measure the realized covariance not only in time but also in frequency domain. Noticeable contribution is brought also by the application of the presented theory. Our time-frequency estimators bring not only more efficient estimates, but decomposes the realized covariation into arbitrarily chosen investment horizons. Results thus bring better understanding of the dynamics of dependence between the stock markets.
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Popis textur pomocí wavelet v systému Nephele
Beneš, Miroslav ; Zitová, Barbara
In our paper we introduce solution for processing information about artwork specimens used in the course of art restoration – Nephele. The archiving part of the Nephele enables creating database entries for painting materials research database, their storage, and creating text-based queries. In addition to these traditional database functions, advanced report retrieval is supported; based on the similarity of image data, comparing either the ultraviolet and visual spectra images, and the electron microscopy images. The wavelet decomposition of the latter images provides basis for material characterization using features computed from the decomposed data.
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