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Dense zeros
Hanousek, Jan ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
This research focuses on a special type of time series data where a significant propor- tion of values is zero. The aim is to develop a statistical model that accurately captures the behavior of such data. By exploring existing theories on GARCH and MEM models, new models together with derivation of important theoretical properties are proposed. To assess their effectiveness, they are tested on real-world data. This evaluation reveals that each model has its own strengths and weaknesses. The overall results are promis- ing, proving the models' validity and real-world applicability, opening doors for further exploration in this area. 1
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Parametric variance modelling within a feasible weighted least squares estimator
Dávidík, Filip ; Hudecová, Šárka (advisor) ; Cipra, Tomáš (referee)
This thesis explores the implications of heteroscedasticity in regression models, where the variance of errors is not constant across observations. Traditional estimators such as Ordinary Least Squares (OLS) rely on the assumption of homoscedasticity, but real-world data often deviate from this ideal. In response, Weighted Least Squares (WLS) estima- tion is introduced to address known forms of heteroscedasticity, alongside the Feasible Weighted Least Squares (FWLS) estimation method, which only requires partial knowl- edge of heteroscedasticity's form. The theoretical contribution establishes the efficiency of the WLS over the OLS under known heteroscedasticity, and the introduction of the FWLS as a viable alternative. Simulation studies further illustrate the nuanced behavior of the FWLS estimators, offering a comprehensive comparison of the various candidate FWLS estimators under varying model specifications (including misspecified variance models) and insights into their performance relative to the OLS estimator. Recommen- dations are provided to guide method selection based on specific model characteristics, highlighting the importance of accounting for heteroscedasticity in empirical research. 1
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Multivariate Volatility Modeling
Jurák, František ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This thesis deals with the formulation and estimation of the multivariate GARCH model. It mentions the various parameterizations of the multivariate GARCH model and discusses the relationships between them. The necessary and sufficient conditions for covariance stationarity of the multivariate GARCH model are presented, as is the maximum likelihood estimation of the parameters of the model. The thesis also includes estimation of the parameters of the bivariate GARCH(1,1) model for real time series using EViews. 1
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Multiline aggregate XL-reinsurance
Šuchová, Martina ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
This paper focuses on simulation modeling of the total aggregate reinsurer claim S when considering XL.reinsurance for multiple insurance lines. In the first part, this re- insurance structure is defined. In the second part of the paper, the collective model is approached, as well as the definition of copulas (comonotony copula, independence co- pula, Clayton's or Gumbelt's copula), and Sklar's theorem. The last part discusses a simulation study that shows the simulation of aggregate claims when considering inde- pendence as well as dependence of insurance industries. The simulation study outlines the theoretical approach in the introduction, explaining the heuristic algorithm it uses in simulating dependent industries. The conclusion of the study depicts one of the practical applications, and the outputs of the simulations. 1
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Additivity of Chain-Ladder method for projection of technical provisions in non-life insurance
Němec, Adam ; Cipra, Tomáš (advisor) ; Kříž, Pavel (referee)
This bachelor thesis deals with the subject of additivity of projections obtained by the Chain Ladder method in the corresponding cumulative development triangles. The reader first gets acquainted with the Chain Ladder method itself and then one presents basic theoretical insights concerning the additivity of projections and the related projection inequality. It also discusses practical interpretation, which it demonstrates us- ing real reinsurance data. Moreover, standard errors of projections in triangles are briefly described in a separate chapter using basic theory of probability and applied in the given numerical study. 1
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Claim inflation in car insurance
Neumann, Vojtěch ; Kříž, Pavel (advisor) ; Cipra, Tomáš (referee)
This thesis explores the practical use of generalized linear models. The aim of the thesis is to analyze the claims inflation for Motor Third Party Liability Insurance. For this purpose, current data from a Czech insurance company are provided. In the thesis, a generalized linear model is constructed in detail based on specified criteria. From the model, the effect of inflation is identified and its value for the given period is determined. 1
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Multivariate volatility forecasts for large portfolios
Vágner, Jan ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
One deals with the estimation and consequent forecast of the integrated covariance matrix in the context of high-frequency stock price data and high dimensionality regarding the number of analyzed assets. We present several methods for the integrated covariance estimation and then use these estimates as a basis for forecasting models. We mainly focus on the multivariate extensions of the HAR model. Finally, in the empirical study, we compare different model-estimator combinations (based on 5-min interval observation and 50 assets) using economic and statistical evaluation. Economic evaluation is based on portfolio optimization, including transaction costs. 1
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Transient behavior of bonus-malus systems
Tichá, Tereza ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
This thesis deals with bonus-malus systems in car insurance. First of all, the basic no- tation is introduced and the principles are described on the basis of which these systems can be modeled using homogeneous Markov chains. The development of bonus-malus systems is usually evaluated using various characte- ristics such as relativity or elasticity, which are calculated on the basis of a stationary distribution. However, these calculations only make sense if the stationarity is reached in a reasonable time. However, for real systems, this time is much longer than the time the driver spends in the portfolio. Therefore, an alternative possibility of evaluation using the age correction of the stationary distribution is propo- sed. Finally, the use of stationary and age-corrected distributions is compared for specific examples in the practical part. 1
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Distributed lag models
Dian, Patrik ; Cipra, Tomáš (advisor) ; Hudecová, Šárka (referee)
The aim of this bachelor thesis is to unite the theory about distribu- ted lag models and autoregressive distributed lag model, which includes lagged dependent variables and application of these models on real data. The properties of these models are also presented. Dynamic models are highly used for financial and economic data because of their ability to capture lagged effect on dependent variable. As a similar topic there are mentioned models of intervention analysis which are used to examine the external effects on time series and to model the in- terventions using indicator variables. Finally, applications of mentioned models on two data sets are introduced and analysis of the effect of coronavirus pandemic on time series is demonstrated. 1
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