This thesis discusses travel time prediction of vehicles on roads based on the methods of machine learning. It describes theory of travel times and summarizes scientific papers dealing with this topic. Within the thesis, analysis of real travel time data was done and the features to be used in prediction models were engineered. Finally, the complex prediction system was designed and implemented and has been tested in production environment.

Most of the literature on Value at Risk concentrates on the unconditional nonparametric or parametric approach to VaR estimation and much less on the direct modeling of conditional quantiles. This thesis focuses on the direct conditional VaR modeling, using the flexible quantile regression and hence imposing no restrictions on the return distribution. We apply semiparamet- ric Conditional Autoregressive Value at Risk (CAViaR) models that allow time-variation of the conditional distribution of returns and also different time-variation for different quantiles on four stock price indices: Czech PX, Hungarian BUX, German DAX and U.S. S&P 500. The objective is to inves- tigate how the introduction of dynamics impacts VaR accuracy. The main contribution lies firstly in the primary application of this approach on Cen- tral European stock market and secondly in the fact that we investigate the impact on VaR accuracy during the pre-crisis period and also the period covering the global financial crisis. Our results show that CAViaR models perform very well in describing the evolution of the quantiles, both in abso- lute terms and relative to the benchmark parametric models. Not only do they provide generally a better fit, they are also able to produce accurate forecasts. CAViaR models may be therefore used as a...

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

Title: Methods of dynamical analysis of portfolio composition Author: Ivana Meňhartová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomáš Hanzák, KPMS, MFF UK Abstract: In the presented thesis we study methods used for dynamic analysis of portfolio based on it's revenues. The thesis focuses on Kalman filter and local- ly weighted regression as two basic methods for dynamic analysis. It describes in detail theory for these methods as well as their utilization and it discusses their proper settings. Practical applications of both methods on artificial data and real data from Prague stock-exchange are presented. Using artificial data we demonstrate practical importance of Kalman filter's assumptions. Afterwards we introduce term multicolinearity as a possible complication to real data applicati- ons. At the end of the thesis we compare results and usage of both methods and we introduce possibility of enhancing Kalman filter by projection of estimations or by CUSUM tests (change detection tests). Keywords: Kalman filter, locally weighted regression, multicollinearity, CUSUM test

This thesis analyses financial contagion between a reference EU market - Germany and markets of five countries which are actively seeking to become a part of European Union - Montenegro, Serbia, Turkey, Bosnia and Macedonia in the period of March 2006 to March 2018. We apply quantile regression framework to analyse contagion which we base on the occurrence and degree of coexceedances between the reference and analysed market. The results indicate that contagion between stock markets exists, however in different degree for each of the analysed markets. In addition we apply the regression framework specifically for period of financial crisis of 2008 to demonstrate that contagion is stronger during turbulent market periods. JEL Classification G01, G14, G15 Keywords coexceedance, quantile regression, contagion, stock markets Author's e-mail 80605682@fsv.cuni.cz Supervisor's e-mail roman.horvath@fsv.cuni.cz

The aim of the masters thesis is comparison of selected demographic indicators that affect ageing population in Czech republic and France. The demographic development is focusing on the period from 2005 to 2015. The theoretical part is focused on literature search. It is devoted to analysis of causes of ageing population on the present and description of demographic statics and dynamics and structure of education. As part of the fulfillment of the objectives of the work will be used in the method of comparison, time series analysis and regression. For 2005-2015 is typical rising average population, ageing of population and higher life expectancy. Despite declining fertility in both countries, France still ranks among the countries with the highest birth rate in the EU

Correctly specified models to forecast returns of indices are important for in- vestors to minimize risk on financial markets. This thesis focuses on conditional Value at Risk modeling, employing flexible quantile regression framework and hence avoiding the assumption on the return distribution. We apply semi- parametric linear quantile regression (LQR) models with realized variance and also models with positive and negative semivariance which allows for direct modelling of the quantiles. Four European stock price indices are taken into account: Czech PX, Hungarian BUX, German DAX and London FTSE 100. The objective is to investigate how the use of realized variance influence the VaR accuracy and the correlation between the Central & Eastern and Western European indices. The main contribution is application of the LQR models for modelling of conditional quantiles and comparison of the correlation between European indices with use of the realized measures. Our results show that linear quantile regression models on one-step-ahead forecast provide better fit and more accurate modelling than classical VaR model with assumption of nor- mally distributed returns. Therefore LQR models with realized variance can be used as accurate tool for investors. Moreover we show that diversification benefits are...

Title: Influence of errors to regression model Author: Bc. Vlasta Poliačková Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Petr Lachout, CSc. Supervisor's e-mail address: Petr.Lachout@mff.cuni.cz Abstract: The submitted work deals with the regression model, and the influence of errors to regression. Thesis describes different types of violations of assumptions re- quired to the error term and their impact to the properties of the regression model. In the next part, there are discussed various statistical approaches applicable in the case of violation assumptions of regression model such as heteroscedasticity or autocor- relation of the residuals. In the application part, there is used mainly knowledge of Box - Jenkins methodology. In this section it is described in detail how to build a Box - Jenkins models and forecasts of future values for various real financial time series. In processing of the data are used models of ARMA, ARIMA and SARIMA. In an example, forecasts of the models are compared to real future values of the time series. Keywords: regression, violation of assumptions, error term, Box-Jenkins methodo- logy, time series

The performance of similarity search in the unstructured databases largely depends on the employed similarity model. The properties of metric space model enable indexing the data with metric access methods efficiently. But for unconstrained or nonmetric similarity models typical for multimedia, medical, or scientific databases, in which metric postulates do not hold, there exists no general solution so far. Motivated by the successful application of Ptolemaic indexing to the image retrieval, we introduce SIMDEX Framework which is a universal framework that is capable of revealing alternative indexing methods that will serve for efficient yet effective similarity searching for any similarity model. It explores the axiom space in order to discover novel techniques suitable for database indexing. We review all existing variants (simple I-SIMDEX; GP-SIMDEX and PGP-SIMDEX which both use genetic programming) and we outline how the different groups of domain researchers can benefit from them. We also describe a real application of SIMDEX Framework to practice while building the Smart Pivot Table indexing method together with advanced Triangle+ filtering for metric spaces empowered by LowerBound Tightening technique. At all cases, we provide extensive experimental evaluations of mentioned techniques. Powered by...

Diplomová práca sa zaoberá detekciou a hodnotením skreslených snímok v retinálnych obrazových dátach. Teoretická časť obsahuje stručné zhrnutie anatómie oka a metód hodnotenia kvality obrazov všeobecne, ako aj konkrétne hodnotenie retinálnych obrazov. Praktická časť bola vypracovaná v programovacom jazyku Python. Obsahuje predspracovanie dostupných retinálnych obrazov za účelom vytvorenia vhodného datasetu. Ďalej je navrhnutá metóda hodnotenia troch typov šumu v skreslených retinálnych obrazoch, presnejšie pomocou Inception-ResNet-v2 modelu. Táto metóda nebola prijateľná a navrhnutá bola teda iná metóda pozostávajúca z dvoch krokov - klasifikácie typu šumu a následného hodnotenia úrovne daného šumu. Pre klasifikáciu typu šumu bolo využité filtrované Fourierove spektrum a na hodnotenie obrazu boli využité príznaky extrahované pomocou ResNet50, ktoré vstupovali do regresného modelu. Táto metóda bola ďalej rozšírená ešte o krok detekcie zašumených snímok v retinálnych sekvenciách.