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Recursive least squares method: Selected applications
Mičuda, Timotej ; Hendrych, Radek (advisor) ; Hudecová, Šárka (referee)
This bachelor's thesis introduces, derives and implements recursive least squares me- thod. The recursive least squares method is analogy to ordinary least squares for linear regression exercise. Method uses recursive procedure to update coefficients. The goal of this work is to introduce the recursive method algorithm and to become familiar with its benefits. We will use the method for three different simulations, where we show selected properties and modifications. Also we apply the method for estimation of real data in connection with CAPM model. 1
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Goodness-of-fit tests for exponential distributions
Hlaváčová, Nikola ; Hudecová, Šárka (advisor) ; Mizera, Ivan (referee)
The thesis deals with goodness-of-fit tests for the exponential distribution. In the first part, basic concepts are introduced, including their properties. Afterwards, goodness-of- fit tests based on the empirical distribution function are presented. These tests are divided depending on whether the parameter of the distribution λ > 0 is known or unknown. If the parameter is unknown, the method of parametric bootstrap is used, where the un- known parameter λ is estimated using the maximum likelihood method. The next section presents tests utilizing some properties of the exponential distribution, such as the Gini index and Mean Residual Life. In this part, the forms of their test statistics and distribu- tions under the assumption of the null hypothesis are derived. Finally, a simulation study is presented that compares individual tests in terms of their level and power for different settings. 1
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Expectiles and their estimates
Škurek, Jan ; Hudecová, Šárka (advisor) ; Kopa, Miloš (referee)
This bachelor's thesis focuses on studying expectiles as an alternative approach to traditional quantiles. Expectiles are becoming increasingly popular as risk measures in various fields, including finance and insurance sectors. The thesis presents basic properties and derivations of expectiles in detail. In addition to the definition of sample expectiles, a parametric estimation method for expectiles is introduced. The practical part is devoted to the estimation of sample expectiles, parametric estimation using the method of mo- ments, and a comparison of both methods on a simulated sample from the exponential distribution. 1
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Estimation of latent distribution for ordinal data
Hržič, Viktor ; Hudecová, Šárka (advisor) ; Komárek, Arnošt (referee)
The main goal of the bachelor thesis is to introduce problematics of ordinal data together with estimations of latent density distribution based on ordinal data. The esti- mations obtained using ordinal data are compared to the ones that are more common and used on daily basis. The reader will be introduced to the maximum likelihood method that is used in the development of each estimate. One chapter is dedicated to alterna- tive approach using Bernstein polynomials. When we take all benefits into account such as easier collecting the data in ordinal form or minimization of possible errors committed by respondent, we obtained very valuable and promising results. 1
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Financial time series models and their software implementation
Kostárová, Aneta ; Zichová, Jitka (advisor) ; Hudecová, Šárka (referee)
This thesis deals with financial time series models and their implementation in soft- ware products. The theoretical part of the thesis includes a description of the volatility models ARCH, GARCH, IGARCH, ARCH-M, GARCH-M, EGARCH and GJR-GARCH and their basic properties. The practical part examines and describes the implementation of the volatility models in the software products Mathematica, EViews and R. Tutorials on the use of each function are included, along with descriptions of the software inputs and outputs in the form of illustrative examples on simulated data and their application to real data. 1
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Goodness-of-fit tests for Poisson distribution based on zero index
Váňová, Julie ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
This bachelor thesis deals with goodness-of-fit tests for Poisson distribution that are based on so-called zero index. In the first part, Poisson zero index is defined and some of its basic properties are discussed. Further, asymptotic distribution of zero indexes is derived and it is used to construct asymptotic goodness-of-fit tests. Particular examples of zero indexes and related tests are included. In the following part, other types of goodness-of-fit tests for Poisson distribution are briefly described, in particular χ2 -tests and tests based on index of dispersion. All mentioned methods are then compared in a simulation study. 1
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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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