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Outliers
Kudrnáč, Vojtěch ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
This paper concerns itself with the methods of identifying outliers in an otherwise normally distributed data set. Several significant tests and criteria designed for this purpose are described here, Peirce's criterion, Chauvenet's criterion, Grubbs' test, Dixon's test and Cochran's test. Deriving of the tests and criteria is indicated and finally the results of the use of the test and criteria on simulated data with normal distribution and inserted outlier are looked into. Codes in programming language R with the implementation of these test and criteria using existing functions are included. Powered by TCPDF (www.tcpdf.org)
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Some problems of exponential smoothing
Čurda, David ; Hanzák, Tomáš (advisor) ; Komárek, Arnošt (referee)
In this work the several exponential smoothing type methods are briefly described, which are often used to smoothing and forecasting in the time series. Selected problems, that occur in described methods, are presented and in some cases there are the suggestions to their solution, which should tend to more suitable smoothing or to the better forecasts. It's shown how the methods are applied on different data and how the forecasts differ from each other. In conclusion the quality of modifications is evaluated.
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Robust estimation of autocorrelation function
Lain, Michal ; Hudecová, Šárka (advisor) ; Hlávka, Zdeněk (referee)
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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L1 Regression
Čelikovská, Klára ; Maciak, Matúš (advisor) ; Hlubinka, Daniel (referee)
This thesis is focused on the L1 regression, a possible alternative to the ordinary least squares regression. L1 regression replaces the least squares estimation with the least absolute deviations estimation, thus generalizing the sample median in the linear regres- sion model. Unlike the ordinary least squares regression, L1 regression enables loosening of certain assumptions and leads to more robust estimates. Fundamental theoretical re- sults, including the asymptotic distribution of regression coefficient estimates, hypothesis testing, confidence intervals and confidence regions, are derived. This method is then compared to the ordinary least squares regression in a simulation study, with a focus on heavy-tailed distributions and the possible presence of outlying observations. 1
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Robust regression - outlier detection
Hradilová, Lenka ; Blatná, Dagmar (advisor) ; Černý, Jindřich (referee)
This master thesis is focused on methods of outlier detection. The aim of this work is to assess the suitability of using robust methods on real data of EKO-KOM, a.s. The first part of the thesis provides an overview and a theoretical treatise on classic and robust methods of outlier detection. These methods are subsequently applied to the obtained data file of EKO-KOM, a.s. in the practical part of the thesis. At the conclusion of the thesis, there are recommendations about suitability of methods, which are based on comparison of classical and robust methods.
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Stable distributions and their applications
Volchenkova, Irina ; Klebanov, Lev (advisor) ; Beneš, Viktor (referee)
The aim of this thesis is to show that the use of heavy-tailed distributions in finance is theoretically unfounded and may cause significant misunderstandings and fallacies in model interpretation. The main reason seems to be a wrong understanding of the concept of the distributional tail. Also in models based on real data it seems more reasonable to concentrate on the central part of the distribution not tails. Powered by TCPDF (www.tcpdf.org)
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Robustification of statistical and econometrical regression methods
Jurczyk, Tomáš ; Víšek, Jan Ámos (advisor) ; Hlávka, Zdeněk (referee) ; Malý, Marek (referee)
Title: Robustification of statistical and econometrical regression methods Author: Mgr. Tomáš Jurczyk Department: Department of probability and mathematical statistics Supervisor: prof. RNDr. Jan Ámos Víšek CSc., IES FSV UK Praha Abstract: Multicollinearity and outlier presence are two problems of data which can occur during the regression analysis. In this thesis we are interested mainly in situations where combined outlier-multicollinearity problem is present. We will show first the behavior of classical methods developed for overcoming one of these problems. We will investigate the functionality of methods proposed as robust multicollinearity detectors as well. We will prove that proposed two-step procedures (in one step typically based on robust regression methods) are failing in outlier detection and therefore also multicollinearity detection, if the strong multicollinearity is present in the majority of the data. We will propose a new one-step method as a candidate for the robust detector of multicollinearity as well as the robust ridge regression estimate. We will derive its properties, behavior and propose the diagnostic tools derived from that method. Keywords: multicollinearity, outliers, robust detector of multicollinearity, ro- bust ridge regression 1
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Outliers
Kudrnáč, Vojtěch ; Zvára, Karel (advisor) ; Anděl, Jiří (referee)
This paper concerns itself with the methods of identifying outliers in an otherwise normally distributed data set. Several significant tests and criteria designed for this purpose are described here, Peirce's criterion, Chauvenet's criterion, Grubbs' test, Dixon's test and Cochran's test. Deriving of the tests and criteria is indicated and finally the results of the use of the test and criteria on simulated data with normal distribution and inserted outlier are looked into. Codes in programming language R with the implementation of these test and criteria using existing functions are included. Powered by TCPDF (www.tcpdf.org)
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Some problems of exponential smoothing
Čurda, David ; Hanzák, Tomáš (advisor) ; Komárek, Arnošt (referee)
In this work the several exponential smoothing type methods are briefly described, which are often used to smoothing and forecasting in the time series. Selected problems, that occur in described methods, are presented and in some cases there are the suggestions to their solution, which should tend to more suitable smoothing or to the better forecasts. It's shown how the methods are applied on different data and how the forecasts differ from each other. In conclusion the quality of modifications is evaluated.
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