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The least weighted squares and its asymptotics
Raušová, Magdaléna ; Víšek, Jan Ámos (advisor) ; Hanus, Luboš (referee)
When there are some influential observations present in a data set (such as outliers or leverage points), the use of some robust method may be desirable for being able to draw relevant conclusions from an econometric analysis. In order to use these methods properly, we need some diagnostic tools. To be able to derive these tools theoretically, we first need to know the form of the asymptotic representation of corresponding estimator. This thesis derives the asymptotic representation of the estimator obtained by the method of least weighted squares under the assumption of heteroskedastic residuals. The tight- ness of the estimator and its asymptotic representation under several levels of contamination is also shown in a simulation study.
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Robustification of regression model with the fixed and random effects
Raušová, Magdaléna ; Víšek, Jan Ámos (advisor) ; Bobková, Božena (referee)
In case of some influential observations in an econometric analysis, the classical methods, such as ordinary least squares, are likely to fail. The problem of outliers and leverage points can be overcome by the robust methods. This thesis studies the use of robust methods for panel data - specifically, the robustified versions of the methods of fixed and random effects utilizing the least weighed squares are studied. After introducing the theoretical background, results of a numerical study are provided. This numerical study is a Monte Carlo study that shows, how the classical and robust methods work under several levels of contamination and also, how the choice of the weight function can influence the results of the methods that utilize the least weighted squares.
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Models of changes in econometric time sequences
Strejc, Petr
This paper is concerned with change-point detection in parameters of econometric regression models when a training set of data without any change is available. There are presented two well- known sequential tests - CUSUM test for linear regression model and a test based on weighted residuals for an autoregressive time series - including their asymptotical properties under certain conditions. Two asymptotically equivalent variance estimators are compared in a finite sample situation using Monte Carlo simulations. There are also presented and compared critical value approximations using different bootstrapping methods and variance estimators. Finally, the weighted residual test is applied on S&P 500 historical data.
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Models of changes in econometric time sequences
Strejc, Petr ; Hušková, Marie (advisor) ; Dvořák, Marek (referee)
This paper is concerned with change-point detection in parameters of econometric regression models when a training set of data without any change is available. There are presented two well- known sequential tests - CUSUM test for linear regression model and a test based on weighted residuals for an autoregressive time series - including their asymptotical properties under certain conditions. Two asymptotically equivalent variance estimators are compared in a finite sample situation using Monte Carlo simulations. There are also presented and compared critical value approximations using different bootstrapping methods and variance estimators. Finally, the weighted residual test is applied on S&P 500 historical data.
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Influence of social politics on fertility rate in specific regions of Czech republic
Dvořák, Josef ; Melzochová, Jitka (advisor) ; Babin, Jan (referee)
Thesis is focused on relationship between fertility rate and tools of state support. The goal is to reveal relationship between these two factors. Partial goal is to discover specific effects of tools of state support in specific regions of Czech republic. I have aimed on research at national level and also specific regions between years 1993-2014. In order to find these relationships I used method that compares differences in development of the fertility rate. After that, I set up regression model solved by method called fixed effects. For specific regions analysis was used OLS method. Model was able to explain more than 80 % of variability. This results can be used for predicting of citizens behavior, when some changes in family allowances occurs. Main finding is, that most motivating tools are parenting allowances and child benefits.
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Mathematical Modelling of Relation between Economic Quantities
Žigárdy, Martin ; Hřebíček, Jiří (referee) ; Chvátalová, Zuzana (advisor)
My work is aimed on creating and on subsequent economical interpretation of mathematical models presenting relations of continual development of PX index (Czech stock index) and continual developments of five important world titles, which are price of the West Texas Intermediate Crude Oil barrel, exchange rate between Dollar and Czech Crown as well as Euro and Czech Crown and indexes DAX (German stock index) and Dow Jones (American stock index). The models are create by using regression analysis and by mathematical software Maple version 12
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Regression methods for statistical analysis of spatial data
Klimprová, Lucie ; Šerák, Petr (referee) ; Michálek, Jaroslav (advisor)
Kriging techniques are regression methods used for evaluation of continuous spatial processes. If the covariance structure of process is unknown, then it's necessary to estimate it from the data. The first part of this Master's thesis is devoted to description the kriging method and to estimate of a variogram fuction, which describes the covariance structure of considered process. The second part includes the implementation of kriging method in MATLAB for simulated and real data.
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Program for Analyzing Economical Data via Mathematical Modeling in Maple
Žigárdy, Martin ; Hřebíček,, Jiří (referee) ; Chvátalová, Zuzana (advisor)
In this diploma thesis I constructed generally usable program for processing economical data through mathematical methods of linear regression in Maple system. Program is used for trend dependency analysis of examined quantities. Via multi-stage algorithmization and implementation of information criterion I created interactive form with user-friendly interface with possibility of straight data import from office suite applications. Functionality of this program is verified on example with specific data collection.
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