
Linear regression model with autocorrelated residuals
Kostka, Ján ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
The aim of this bachelor thesis is to introduce the algorithm for analysis of the linear regression model with autocorrelated residuals, which is applicable to time series data. For residuals, we assume the ARMA model, eventually ARIMA model, which enlarges the possibilities of application. The analysis of such regression models includes detection of autocorrelation and related tests, detection of stationarity and related unit root test, followed by model identification for residuals and maximum likelihood estimation of identified regression model.


Change detection in RCA models
Biolek, Jiří ; Prášková, Zuzana (advisor) ; Hudecová, Šárka (referee)
The thesis describes Random Coefficient Autoregressive time series mo dels (RCA models). In first chapter we introduce different types of estimati ons for coefficients of RCA model. Main part is in second chapter, where we describe detection changes procedures for all methods mentioned in chapter one, here the thesis expands the current theory about change detection of wei ghted least square method and functional estimation. In last chapter we sum marize results of simulation study. 1


Markov binomial model
Šuléřová, Natálie ; Hudecová, Šárka (advisor) ; Dvořák, Jiří (referee)
In this thesis we study the Markov chain binomial model, which generalizes the standard binomial distribution. Instead of the sum of independent random vari ables, we consider the sum of random variables that form a stationary Markov chain. The goal of this thesis is to describe this model along with its proper ties, such as the expected value, variance and probability generating function. A part of this thesis is dedicated to estimating parameters of this model using the method of moments and the maximum likelihood estimation. The accuracy of the methods is compared in a simulation study and obtained results are dis cussed. The presented model is then applied on a real dataset based on rate of alcoholimpaired car accidents.


Basic stochastic epidemic models
Strachoňová, Karla ; Hudecová, Šárka (advisor) ; Kulich, Michal (referee)
This thesis deals with two basic models which are used for epidemic model ling in closed populations, namely Greenwood and ReedFrost models. At first, knowledge which a reader needs to have about Markov chains and random varia bles is summarized. Then the two models are described by modelling the number of susceptible and infectious individuals, as well as the duration and size of the epidemic. All of these approaches to modelling an epidemic are then illustrated on examples. Finally, the maximum likelihood method of the probability of infection is described and illustrated on real data in the last chapter, where the obtained results are discussed as well. 1


Poisson autoregression
Böhmová, Karolína ; Hudecová, Šárka (advisor) ; Hlubinka, Daniel (referee)
This thesis deals with INGARCH models for a count time series. Main emphasis is placed on a linear INARCH model. Its properties are derived. Several methods of estimation are introduced  maximum likelihood method, least squares method and its modifications  and later compared in a simulation study. Main properties and maximum likelihood estimation for INGARCH(1,1) model are stated. Higher order linear INGARCH models and nonlinear INGARCH models are discussed briefly. An application of the presented models on time series of car accidents is given.


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


Tests for Combination of Correlation Coefficients
Kulíšková, Michaela ; Hudecová, Šárka (advisor) ; Pešta, Michal (referee)
This bachelor thesis is focused on tests for correlation coefficients. Fundamental knowledge about correlation coefficient are reminded as well as tests for correlation coefficient based on estimated correlation coefficient. Then three main methods for combining more correlation coefficients  Fisher`s method, Linear combination test with Ztransformation and Hotelling transformation  are described, simulated and compared. These tests have several assumptions such as that k correlation coefficients are known as well as the range of random samples from which they were calculated plus it is assumed that these correlation coefficients are equal.


Econometric Modelling and Forecasting of Natural Gas Spot Prices
Kubišová, Barbora ; Hendrych, Radek (advisor) ; Hudecová, Šárka (referee)
The thesis deals with modeling and forecasting of natural gas spot prices, con sumption of natural gas and average daily temperature. We assume that these three variables are influenced by each other, because as temperature decreases, consumption increases, which in turn increases the price with the increasing de mand. Therefore, we propose to model these variables by vector autoregression. We compare this model with onedimensional models where for each one we build a model from the ARMAGARCH class. Models are estimated using historic va lues and then designed models are used to simulate scenarios. Analysis of scenarios provides information to gas supply companies estimates of portfolio consumption and financial flows related to the purchase concerning natural gas. 1


Special aspects of nonlinear time series modelling
Studnička, Václav ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
Various models, such as ARMA and GARCH, are used in the financial time series framework. The purpose of this thesis is to present an alternative for these models which are bilinear time series models. First chapter is theore tical, there is a short introduction to the theory of time series and ARMA models. Second chapter focuses on theoretical aspects of the simple bilinear model, third chapter presents the theory for general bilinear model in the similiar fashion as for simple model. Last chapter is focused on practical aspects, it contains simulations and examines the properties of estimates based on the presented theory, final part is devoted to the comparison of properties of ARMA models and bilinear models for selected financial data. 1


Measures of extremal dependence in time series
Popovič, Viktor ; Pawlas, Zbyněk (advisor) ; Hudecová, Šárka (referee)
In the present thesis we deal with dependence among extremal values within time series. Concerning this type of relations the commonly used autocorrelation function does not provide sufficient information. Moreover, autocorrelation function is suitable for Gaussian processes while nowadays we often work with heavytailed time series. In this thesis we cover two measures of extremal dependence that are used for this type of data. We introduce the coefficient of tail dependence, measure of extremal dependence based on tail characteristics of joint survival function. The second measure is called extremogram, which depends only on the extreme values in the sequence. In addition to the theoretical part, simulation study and application to real data of both described measures including their comparison are performed. Results are stated together with tables and graphical output.
