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Clustering and regression analysis of micro panel data
Sobíšek, Lukáš ; Pecáková, Iva (advisor) ; Komárek, Arnošt (referee) ; Brabec, Marek (referee)
The main purpose of panel studies is to analyze changes in values of studied variables over time. In micro panel research, a large number of elements are periodically observed within the relatively short time period of just a few years. Moreover, the number of repeated measurements is small. This dissertation deals with contemporary approaches to the regression and the clustering analysis of micro panel data. One of the approaches to the micro panel analysis is to use multivariate statistical models originally designed for crosssectional data and modify them in order to take into account the within-subject correlation. The thesis summarizes available tools for the regression analysis of micro panel data. The known and currently used linear mixed effects models for a normally distributed dependent variable are recapitulated. Besides that, new approaches for analysis of a response variable with other than normal distribution are presented. These approaches include the generalized marginal linear model, the generalized linear mixed effects model and the Bayesian modelling approach. In addition to describing the aforementioned models, the paper also includes a brief overview of their implementation in the R software. The difficulty with the regression models adjusted for micro panel data is the ambiguity of their parameters estimation. This thesis proposes a way to improve the estimations through the cluster analysis. For this reason, the thesis also contains a description of methods of the cluster analysis of micro panel data. Because supply of the methods is limited, the main goal of this paper is to devise its own two-step approach for clustering micro panel data. In the first step, the panel data are transformed into a static form using a set of proposed characteristics of dynamics. These characteristics represent different features of time course of the observed variables. In the second step, the elements are clustered by conventional spatial clustering techniques (agglomerative clustering and the C-means partitioning). The clustering is based on a dissimilarity matrix of the values of clustering variables calculated in the first step. Another goal of this paper is to find out whether the suggested procedure leads to an improvement in quality of the regression models for this type of data. By means of a simulation study, the procedure drafted herein is compared to the procedure applied in the kml package of the R software, as well as to the clustering characteristics proposed by Urso (2004). The simulation study demonstrated better results of the proposed combination of clustering variables as compared to the other combinations currently used. A corresponding script written in the R-language represents another benefit of this paper. It is available on the attached CD and it can be used for analyses of readers own micro panel data.
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Accelerated Linear Genetic Programming in Hardware
Ťupa, Josef ; Bidlo, Michal (referee) ; Sekanina, Lukáš (advisor)
The aim of this thesis is to design and implement hardware acceleration of linear genetic programming for symbolic regression. The thesis contains a theoretical introduction into the studies of modern hardware and genetic programming design. Design and implementation of the LGP for symbolic regression is described in the rest of the thesis.
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Tests for Multiple Changes in Linear Regression Models
Marušiaková, Miriam ; Hušková, Marie (advisor) ; Prášková, Zuzana (referee) ; Picek, Jan (referee)
We consider tests for multiple structural changes in linear regression models. The tests are based on F-type test statistics for the null hypothesis of no change against k changes or against an unknown number of changes with a given upper bound. We extend the existing results to linear regression models with deterministically trending regressors. Moreover, we introduce a generalized M-type test statistic which is based on functionals of weighted M-residuals. In change-point analysis approximations to critical values are usually obtained through the limit behavior of the respective test statistic under the null hypothesis. However, these approximations are often not satisfactory. Either the convergence of the test statistic to its limit distribution is rather slow or the limit distribution itself is very complex. An alternative approach is to apply resampling methods. We explore this possibility for F-type and M-type test statistics in the presence of multiple change points. We prove that the bootstrap method provides asymptotically correct critical values for the studied tests. We conduct several simulation experiments to show that the bootstrap based approximations are reasonable also in nite sample situations. Moreover, these approximations are often better than the asymptotic critical values. Finally, we...
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Return and risk analysis in the selected industries
VELEBOVÁ, Anna
This thesis deals with the analysis of the profitability and risk of selected sectors on a stock exchange. For analysis of the industry period of 5 years was selected. This period begins in January 2010 and ends in December 2014. Data for the analysis were obtained from the New York Stock Exchange. Ratings industry is based on key indicators of profitability and risk. The profitability of the sector was calculated average and total. The risk was assessed by standard deviation, variance and coefficient of variation. The next step was to evaluate the sector by pricing model of capital asset. The coefficients alpha and beta were obtained by linear regression. MS Excel software was used for calculation. The first part describes the capital market, its subjects and the stock exchanges. For assessing the shares the basic formulas for calculating profitability, risk and CAPM are described in the theoretical part. Methodology paper describes the procedure for evaluating stocks and sectors. There is described a precise procedure of calculating individual indicators. In the third section the results of the analyzed sectors are evaluated. There is described the risk assessment of the industry and the future development of the sector. In conclusion the capital market and forecast of its development are evaluated.
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The equations, systems of equations and polynomials on secondary school curriculum
KOHOUTOVÁ, Veronika
The aim of this thesis is to write a collection of mathematics exercises which should make an important aid for grammar school teachers and pupils. This collection can serve as remedial education to (weaker) pupils. The collection is dividend into four chapters the linear equations, system of linear equations, polynomials and word problems. These chapters contain a brief description, examples with solutions and unsolved examples, bonus tasks and results are at the end of these chapter.
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Studium klimatických změn v České republice
Osičková, Renata
In my Diploma Thesis are processed and analyzed values of average monthly temperatures recorded in 34 meteorological stations that are uniformly distributed in the territory of the Czech Republic. Recorded data are approximated by a series regression function F(t, x, y, h), which is based on a model . This function describe the dependence of temperature T [°C] on time t [year], geographical position x, y [km] and altitude h [m]. Unknown coefficients of the linear functions were calculated using a Maple application based on the method of least squares. The author calculated coefficients of linear correlation for each meteorological station and also the time development of the coefficient of linear correlation for the whole territory of the Czech Republic. The calculated average values for individual stations and for the whole territory were 0.97 and 0.92, respectively. This result indicates a very high standard of the developed model and the model itself indicates that the average temperatures are decreasing in approximately 80 % of the territory of the Czech Republic.
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Assessment of the development of milk prices in selected EU countries
BICKOVÁ, Miroslava
Objective of this thesis was to describe and evaluate the development of milk prices in selected countries of the European Union and The Czech Republic. The theoretical part describes the definition of price, pricing, division of prices, factors affecting the consumption of milk, the connection between consumption, price and income. The thesis also analyzes the particularities of agricultural prices compared with prices in other sectors. It was drawn from literature of Czech and foreign authors. In the methodical part there are described statistical and economic calculation methods. The development of milk prices in each selected EU countries is described in the practical part. Analyzed countries were not chosen randomly. In this paper, there are selected three old states (Denmark, Italy, United Kingdom) and three new states (Lithuania, Poland and Slovakia) and of course the Czech Republic. Furthermore, the price development is assessed by means of price indexes, using analysis of longer time series. In the longer term series there is used the time series analysis, where a linear trend is modeled and a verification of the correctness of the predicted trend results is made. The time series is also examined from the viewpoint of seasonal fluctuations. The thesis is more interested in the national environment, efficiency of large milk producers. In the third part there is calculated the dependence of price development on income situation in each country and the impact of prices on consumption. Coefficients of income elasticity and elasticity of consumption were used. Price and income elasticity was compared in each country of the EU. The conclusion contains summary of results and performed discussion.
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Investigatiom of friction on a beam-blades model
Půst, Ladislav ; Veselý, Jan ; Horáček, Jaromír ; Radolfová, Alena
Results of measurements of damping and friction properties of a couple of turbine blades modeled by a couple of cantilever prismatic beams with perpendicular branches provided by friction surfaces made of material T671- Böhler or coating of wolfram carbide are presented. The dependences of energy lost, coefficients of dry friction and equivalent linear damping coefficients on amplitudes of vibrations, on frequency in the range 10 – 40 Hz and on normal forces were shown. Revided regression relation can be used at damping elements designed of turbine blades.
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