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Modelling dependence between hydrological and meteorological variables measured on several stations
Turčičová, Marie ; Jarušková, Daniela (advisor) ; Hlávka, Zdeněk (referee)
Title: Modelling dependence between hydrological and meteorological variables measured on several stations Author: Bc. Marie Turčičová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Daniela Jarušková CSc., Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics Abstract: The aim of the thesis is to explore the dependence of daily discharge averages of the Opava river on high daily precipitation values in its basin. Three methods are presented that can be used for analyzing the dependence between high values of random variables. Their application on the studied data is also given. First it is the tail-dependence coefficient that measures the dependence between high values of two continuous random variables. The model for the high quantiles of the discharge at a given precipitation value was first determined non-parametrically by quantile regression and then parametrically through the peaks-over-threshold (POT) method. Keywords: extremal dependence, tail-dependence coefficient, quantile regression, peaks over threshold method
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Statistical inference based on saddlepoint approximations
Sabolová, Radka ; Jurečková, Jana (advisor) ; Hlávka, Zdeněk (referee) ; Picek, Jan (referee)
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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Statistical inference based on saddlepoint approximations
Sabolová, Radka
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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An Empirical Investigation of Wage Discrimination in Professional Football
Blaha, Jakub ; Kocourek, David (advisor) ; Jonášová, Júlia (referee)
Salary discrimination is a phenomenon that arises from ineffective behaviour of economic subjects. Even though its presence is incompatible with the the- ory of profit maximization, salary inequality still persists in the human society. Nevertheless, the investigation of this topic has been largely unheeded in the environment of professional football. In our empirical research, we use the most recent data to investigate the salary gap between white, African American and Hispanic players in the American Major League Soccer. Besides ordinary least squares method that focuses on the impact of ethnicity for the average player, we adopted the method of quantile regression to reveal wage gap between play- ers with below-average pays. Observing each player's performance for 3 seasons, we uncovered salary discrimination against African Americans and Hispanics in the lowest decile of the salary distribution that amounts to 18.9% and 15.3%, respectively. Furthermore, we utilized the difference-in-differences (DID) esti- mator to find no effect of the increasing level of invested money on the wage gap. JEL Classification J30, Z20, Z21, J71 J31 J15 Keywords discrimination, race inequality, football, quan- tile regression, OLS, wages, racism Author's e-mail kubablaha@seznam.cz Supervisor's e-mail kocourek.david@email.cz
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Analysis of contagion between energy and CEE financial markets
Kosar, Mariia ; Horváth, Roman (advisor) ; Geršl, Adam (referee)
This work analyzes the contagion effects between energy and CEE financial markets during the two crisis periods (global financial crisis 2008-2009 and energy market crisis 2014), using a sample of daily data from 2004 till 2015. We detect contagion by observing the degree and structure of two dummy variables for specified crisis periods included into the quantile regression models on the basis of a dependence measure called "coexceedances". Our results show that there are significant contagion effects present between the gasoil and CEE stock markets during the 2008-2009 period and mixed evidence of contagion between crude oil market and CEE stock markets. CEE stock markets do not appear to exhibit significant contagion effects with energy markets during the recent energy market crisis. These results substantially differ from those found in the developed European markets. In particular, our results indicate that energy markets and stock markets in developed Europe seem to display significant contagion effects during the 2014-2015 period. Keywords: Central and Eastern Europe, contagion, energy market, quantile regression
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Understanding systematic risk of assets at various quantiles of return distribution 
Rusý, Tomáš ; Baruník, Jozef (advisor) ; Avdulaj, Krenar (referee)
In this thesis, we deal with the application of quantile regression to the Capital Asset Pricing Model, which is derived in the thesis. We investigate a real dataset to determine if one of many implications - constant beta at different quantiles of return distribution, of the model is met. For that purpose, we use Khmaladze test which is perfectly suited for testing if asset's beta varies over return distribution. Before we run the test we introduce both quantile regression and the Khmaladze test to the reader in simple and clear notation as we do not expect the reader to be familiar with this regression technique. Powered by TCPDF (www.tcpdf.org)
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Statistical inference based on saddlepoint approximations
Sabolová, Radka
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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Statistical inference based on saddlepoint approximations
Sabolová, Radka ; Jurečková, Jana (advisor) ; Hlávka, Zdeněk (referee) ; Picek, Jan (referee)
Title: Statistical inference based on saddlepoint approximations Author: Radka Sabolová Abstract: The saddlepoint techniques for M-estimators have proved to be very accurate and robust even for small sample sizes. Based on these results, saddle- point approximations of density of regression quantile and saddlepoint tests on the value of regression quantile were derived, both in parametric and nonpara- metric setup. Among these, a test on the value of regression quantile based on the asymptotic distribution of averaged regression quantiles was also proposed and all these tests were compared in a numerical study to the classical tests. Finally, special case of Kullback-Leibler divergence in exponential family was studied and saddlepoint approximations of the density of maximum likelihood estimator and sufficient statistic were also derived using this divergence. 1
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Modelling dependence between hydrological and meteorological variables measured on several stations
Turčičová, Marie ; Jarušková, Daniela (advisor) ; Hlávka, Zdeněk (referee)
Title: Modelling dependence between hydrological and meteorological variables measured on several stations Author: Bc. Marie Turčičová Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Daniela Jarušková CSc., Czech Technical University in Prague, Faculty of Civil Engineering, Department of Mathematics Abstract: The aim of the thesis is to explore the dependence of daily discharge averages of the Opava river on high daily precipitation values in its basin. Three methods are presented that can be used for analyzing the dependence between high values of random variables. Their application on the studied data is also given. First it is the tail-dependence coefficient that measures the dependence between high values of two continuous random variables. The model for the high quantiles of the discharge at a given precipitation value was first determined non-parametrically by quantile regression and then parametrically through the peaks-over-threshold (POT) method. Keywords: extremal dependence, tail-dependence coefficient, quantile regression, peaks over threshold method
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Měření finanční nákazy pomocí CAViaR metody: Aplikace na Evropu
Tomanová, Petra ; Zouhar, Jan (advisor) ; Formánek, Tomáš (referee)
The aim of this thesis is to measure changes in dependencies among returns on equity indices for European countries in tranquil periods against crisis periods and to investigate their asymmetries in the lower and upper tail of their distributions. The approach is based on a conditional probability that a random variable is lower than a given quantile while other random variables are also lower than their corresponding quantiles. Time-varying conditional quantiles are modeled by the Conditional Autoregressive Value at Risk via Regression Quantiles (CAViaR) method. In addition to the univariate conditional autoregressive models, the vector autoregressive extension is considered. In the second step, the conditional probability is estimated through the OLS regression. Moreover, the model which allows the distribution of returns in one country to lead or to lag the distribution of returns in another country, is defined and applied on European equity returns. Finally, the model measuring dependencies among more than two return series is derived and the relating dimensionality problems are discussed. The results document a significant increase in European equity return comovements in bear markets during the crisis in 1990s and 2000s. The explicit controlling for the high volatility days does not appear to have an impact on the main findings. For the comparison purposes, the results for Latin American countries are reported as well.
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