
Models of binary time series
Kunayová, Monika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
This bachelor thesis deals with the time series of binary variables that exist in many social spheres. The indicator may denote a certain value being exceeded or a phenomenon occurring. We study a model of logistic autoregression and its properties, partial likelihood function which allows us to work with dependent data, and derive useful relationships for a practical application that consists of time series simulation and real data analysis using free software R.


Recursive estimates of financial time series
Vejmělka, Petr ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This work aims to describe the method of recursive estimation of time series with conditional volatility, used mainly in finance. First, there are described the basic types of models with conditional heteroskedasticity (GARCH) and princi ples of statespace modeling demonstrated by means of linear models AR and ARMA. Subsequently, there are derived algorithms for recursive estimation of parameters of the GARCH model and its possible modifications including the ones for which recursive estimation formulas have not been yet derived in lit erature. These algorithms are tested in a simulation study, where their appli cability in practice is investigated. Finally, we apply these algorithms to real highfrequency data from the stock exchange. The practical part is done us ing the software Mathematica 11.3. The work also serves as an overview of the current state of online modeling of financial time series. 1


Multivariate claim numbers models
Zušťáková, Lucie ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
Multidimensional frequency models can be used for modeling number of claims from different branches which are somehow dependent on each other. As in the onedimensional case Poisson distribution and negative binomial distribution are primarily used for modeling multidimensional claim counts data, only they are extended to higher dimensions. The generalization of multi dimensional distributions is often done using socalled shock variables, where one random variable is included in all dimensions of a random vector which models claim counts. The more comprehensive approach to modeling dependence uses copulas. Comparison of these models is done on a simulated data of number of claims from two different car insurance guarantees.


Seasonal mortality and its application in life insurance
Srnáková, Andrea ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
Assumptions like uniform distribution, constant force of mortality and the Balducci assumption frequently used for modeling mortality data do not reflect the variability of monthly death rates. Often a phenomenon of winter excess mortality occurs, which is not respected by these assumptions. We shall apply a seasonal mortality assumption, which uses nonnegative trigonometric sums for modeling the distribution of monthly death rates. We then apply our findings to the Czech mortality data. We calculate monthly premiums in a shortterm life insurance policy and compare the result with results given by the classical assumptions. 1


Counterparty risk in reinsurance
Kohout, Marek ; Cipra, Tomáš (advisor) ; Pešta, Michal (referee)
The main goal of this Bachelor thesis is to present a survey of methods for cal culating the required capital to cover the default risk of reinsurers in the frame work of the regulatory system Solvency II in EU. The methods are based on socalled common shock principle which is preferred in the case of portfolios with a smaller number of heterogeneous counterparties (e. g. reinsurers). In difference from (Hendrych and Cipra, 2018) the case with flexible weights of particular reinsurers given by their LGD (loss given default) is considered. One discusses the results of extensive numerical study comparing particular methods. 1


Moving averages in time series
Uhliarik, Andrej ; Cipra, Tomáš (advisor) ; Hudecová, Šárka (referee)
This thesis focuses on time series analysis usikng methods based on moving averages, especially the method based on the approximation of the trend compo nent of a time series by polynomial functions. In the theoretical part of the thesis, we describe procedures for choosing right weights, degree and length of moving average for a specific time series. In the practical part, we are demonstrating this process on real data. A part of the thesis is a simple software for smoothing time series and tables with weights of moving averages for specific degrees and lengths. 1


Parametric Nonlinearity Testing in Time Series
Kollárová, Dominika ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The aim of this bachelor thesis is the theoretical description of the functioning of two parametric nonlinearity tests  the RESET test and Keenan's test and theirs application on financial time series with the summary of achieved results. During the testing we assume, that a time series follows a predetermined linear AR(p) model the order of which is identified by the partial autocorrelation function or the AIC criterion.


Mortality in high ages
Malá, Kateřina ; Mazurová, Lucie (advisor) ; Cipra, Tomáš (referee)
In this thesis, we study modelling of mortality in high ages by several approaches. Some of mentioned models take into account the phenomenon of mortality deceleration. Further, we present several ways of estimating of exposed to risk in (almost) extinct cohorts. We focus especially on the survivor ratio method but we also mention the MD method and the DG method. Finally, we perform a numerical study.


Seasonal exponential smoothing
Rábek, Július ; Cipra, Tomáš (advisor) ; Zichová, Jitka (referee)
This thesis deals with the issues of time series modeling, where seasonal component is present. Principles of basic seasonal exponential smoothing methods: simple and double exponential smoothing, Holt's method, which are applicable on time series without seasonality, are described in the beginning. For seasonal time series, HoltWinters exponential smoothing is the most suitable method. This method is introduced in both of its versions and the usage of either version depends on the characteristics of the seasonal component. Furthermore, state space modeling is presented as a statistical framework for exponential smoothing methods, joined with a discussion of some selected problems related with practical implementation of these techniques together with suggestions of their solution. Finally, HoltWinters method on two real data time series with seasonality is presented.


Ensemble learning methods for scoring models development
Nožička, Michal ; Witzany, Jiří (advisor) ; Cipra, Tomáš (referee)
Credit scoring is very important process in banking industry during which each potential or current client is assigned credit score that in certain way expresses client's probability of default, i.e. failing to meet his or her obligations on time or in full amount. This is a cornerstone of credit risk management in banking industry. Traditionally, statistical models (such as logistic regression model) are used for credit scoring in practice. Despite many advantages of such approach, recent research shows many alternatives that are in some ways superior to those traditional models. This master thesis is focused on introducing ensemble learning models (in particular constructed by using bagging, boosting and stacking algorithms) with various base models (in particular logistic regression, random forest, support vector machines and artificial neural network) as possible alternatives and challengers to traditional statistical models used for credit scoring and compares their advantages and disadvantages. Accuracy and predictive power of those scoring models is examined using standard measures of accuracy and predictive power in credit scoring field (in particular GINI coefficient and LIFT coefficient) on a real world dataset and obtained results are presented. The main result of this comparative study is that...
