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Center-outward ranks and signs and their application in statistical tests
Roubínová, Veronika ; Hudecová, Šárka (advisor) ; Hlubinka, Daniel (referee)
This thesis describes the theory of multivariate rank tests based on center-outward ranks and signs. The definition of the center-outward ranks and signs is based on the measure transportation problem and depends highly on the chosen underlying grid. Sev- eral ways to generate such grids are suggested. Center-outward ranks and signs are then used to construct various test statistics for one-sample testing of location. The main contribution of the work is the introduction of new variants of the one-sample test of location. The proposed test statistics are based on randomized signs and added zero with the usage of the permutation tests for obtaining p-values. The tests are constructed under the assumption of both central or angular symmetry of the underlying distribution. In the end, a simulation study is performed to illustrate the performance of the proposed tests under different settings for several alternatives. 1
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Dynamic panel data models
Lipavská, Kateřina ; Hudecová, Šárka (advisor) ; Hušková, Marie (referee)
This thesis deals with a dynamic panel data model and parameters estimation in these models. First, estimation of parameters in linear regression models is revised as well as ge- neralized method of moments. Second, classical estimation methods for panel data model are considered and it is shown why they are inappopriate to use for dynamic panel data model. Subsequently, two-stage least squares estimation method and estimators based on generalized method of moments are presented, namely Arellano-Bond, Arellano-Bover and Ahn-Schmidt estimators. Some of the theoretical results are illustrated in a Monte Carlo simulation study, which also compares behaviour of the presented estimators under various settings. 1
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Copula based models for multivariate time series
Šír, David ; Hudecová, Šárka (advisor) ; Omelka, Marek (referee)
The thesis deals with the modelling of multivariate time series. The SCOMDY model is described. It models individual univariate time series using an ARMA-GARCH, and their dependence structure is modelled using a copula. For copula selection goodness-of- fit test is discussed. Predictions are presented with algorithms for constructing prediction intervals. The whole theory is demonstrated with examples. Monte Carlo simulations verify the suitability and applicability of the theory. The SCOMDY model is applied to a three-dimensional time series consisting of the closing prices of stocks of Apple Inc. Microsoft Corporation and Alphabet Inc. 1
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Alternative estimators for ARMA-GARCH models
Mašát, Filip ; Hudecová, Šárka (advisor) ; Prášková, Zuzana (referee)
GARCH models are used to describe the volatility of time series. GARCH processes are usually estimated by maximum likelihood or by maximum quasi-likelihood method. However, as these methods require knowledge of the distribution of the innovations or the existence of their fourth moment, they are not always suitable. Several alternative methods that could be an appropriate alternative to classical estimators are described in this thesis. Those estimators are: least squares estimators, weighted Lp estimators and least absolute deviations estimator with logarithmic transformation. These estimators are compared in a simulation study for various settings. A real data application is provided as well. 1
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Time reversibility of random process
Paclík, Ondřej ; Hlubinka, Daniel (advisor) ; Hudecová, Šárka (referee)
Random processes can be used to describe the evolution of a real systems over time. Discrete-time Markov chains are random processes that meet special assumptions, but they still have a lot of practical applications. Some chains have the property that it is impossible to tell if they are being observed when the passage of time is reversed. We call such chains time reversible. In this paper, we define a time reversible Markov chain with discrete time, we show how it can be verified that a given chain is time reversible, and we introduce basic properties and examples of time reversible chains. At the same time, we apply the knowledge of time reversibility to the problem of finding the stationary distribution of specific Markov chains. 1
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Independence testing for series of Poisson variables
Jurčo, Tomáš ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
This thesis deals with tests of independence for time series of identically distributed Poisson random variables. In the introductory part, important terms and definitions are defined, in particular the autocorrelation function, its estimates and INAR(1) model. Three types of tests of independence are described in the thesis - tests based on estimates of the autocorrelation function, simple runs test and tests based on contingency tables. These tests are compared in a simulation study under the null hypothesis of independence and under the alternative of INAR(1) model. 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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Robust estimation of autocorrelation function
Lain, Michal ; Hudecová, Šárka (advisor)
The autocorrelation function is a basic tool for time series analysis. The clas- sical estimation is very sensitive to outliers and can lead to misleading results. This thesis deals with robust estimations of the autocorrelation function, which is more resistant to the outliers than the classical estimation. There are presen- ted following approaches: leaving out the outliers from the data, replacement the average with the median, data transformation, the estimation of another coeffici- ent, robust estimation of the partial autocorrelation function or linear regression. The thesis describes the applicability of the presented methods, their advantages and disadvantages and necessary assumptions. All the approaches are compared in simulation study and applied to real financial data. 1
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Combining multivariate volatility forecasts in portfolio optimization
Šípka, Stanislav ; Hendrych, Radek (advisor) ; Hudecová, Šárka (referee)
The selection of the best-performing model is always a challenge when solving financial-economic problems. The final model might prove to be suboptimal even after a short time if the economic climate changes suddenly. This thesis aims to construct a final model capable of estimating large-scale covariance matrices via the utilization of time-varying weights. A set of multivariate GARCH mod- els to be used as an input in the final combined estimate is used to introduce a weighting scheme based on the metrics of risk-adjusted return of the individ- ual model portfolios. As large-scale modeling often faces problems connected with the underlying dimensionality, the composite likelihood approach to model parameter estimation is proposed as a solution and compared to the standard maximum likelihood and its SVD modification. The resulting weighted covari- ance matrix prediction is used to construct optimal portfolios and their properties are compared in an empirical study. The thesis is concluded by noting the real-life limitation and possible improvements of the defined investing methodology. 1
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