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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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ARFIMA time series models
Vdovičenko, Martin ; Hudecová, Šárka (advisor) ; Prášková, Zuzana (referee)
The thesis deal with long-memory processes which are defined by several ways. The main concern is dedicated to ARFIMA model, to its basic properties and its application. Next, graphical, semiparametric and parametric estimation methods of ARFIMA parameters are described in detail. Five selected R packages are introduced that are suitable for modeling long-memory processes. We discuss their basic functions with description of input arguments and output. Finally, the application of the packages on real data is discussed according to results of~each function. Data sample comes from the Nile River and represents its yearly minimal water levels. Powered by TCPDF (www.tcpdf.org)
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Bootstrap methods for dependent observations
Petrásek, Jakub ; Prášková, Zuzana (advisor) ; Kaňková, Vlasta (referee)
This Diploma thesis deals with principles, asymptotic properties and comparison of bootstrap methods for dependent observations. In the first chapter principal ideas and benefits of bootstrap method for independent data are introduced. Subsequently, these knowledge are applied to data exhibiting dependency. Block, frequency and sieve bootstrap methods are presented. Afterwards, principle of each method is described in broader context, asymptotic properties are presented and some of them are derived. Strong dependency of block bootstrap method on block length is discussed and algorithms for empirical choice of optimal block length are described. The main aim of this work is to compare discussed methods from theoretical point of view and via simulation study. Eventually, a few examples, which are based on real data sets, are presented. Discussed principles are implemented in software R and software Fortran.
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Methods of longitudinal data analysis
Jindrová, Linda ; Volf, Petr (advisor) ; Prášková, Zuzana (referee)
Práce se zabývá longitudinálními daty - měřeními, která jsou prová- děna opakovaně na stejných subjektech. Popisuje r·zné typy model·, které jsou vhodné pro jejich analýzu. Postupuje od nejjednodušších lineárních model· s pevnými nebo náhodnými efekty, přes lineární a nelineární modely se smíšenými efekty, až ke zobecněným lineárním model·m a generalized estimating equati- ons (GEE). Vždy je uveden tvar modelu a zp·sob odhadu parametr·. Jednotlivé modely jsou také porovnávány mezi sebou. Teoretické poznatky jsou doplněny aplikacemi na reálná data. Pomocí lineárních model· analyzujeme data o výrobě v USA, nelineární modely využijeme k vysvětlení závislosti koncentrace léčiva v krvi na čase a GEE aplikujeme na data týkající se dýchacích potíží u dětí. 1
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Structural changes of economic variables
Nerglová, Eva ; Prášková, Zuzana (advisor) ; Marušiaková, Miriam (referee)
Nazev prace: Strukturalni zmeny ekonomickych vclicin Autor: Eva Nerglova Katedra: Katedra pravdepodobnosti a,matematickc statistiky Vcdouci diplomove prace: Doc. RNDr. Zuzana Praskova,CSc. e-mail vedouciho: Zuxana.PraskovHMmff.runi.c-/, Abstrakt: Tato prace se zabyva. detekci zmen ve stfedni hodnote (v poloze) v posloupnosti nonnalne rozdelenych nahodnych vclicin a detckci zmen v jednoduchem inodelu linearni regrese (dvoufazovy rcgresni model). Vedle tcstovani hypote/y o ])fitoniuosti /nieny v uvazovanein inodelu se zabyva i od- hadeni bodu zineiiy a odhadein ])aranictru modelu prod a po zinene. Zabyva se zejmena bayesovsk_yni ])fistupein, v zaveru prace je zininen i pfistuj) zalozcny na metode inaximalni verohodnosti. Oba pfistii])y jsou porovnariy na shnulovaiiych i realnych datecli. Klicova slova: Strukturalni zmena. bod zineny, test stability, bayesovska analyza, inenici se nonnalni poslou]>nost7 dvoufazovy regresni model, metoda niaximalni verohodnosti Title: Structural changes of economic variables Author: Eva Nerglova Department: Department of Probability and Mathematical Statistics Supervisor: Doc. KXDr. Zuzana Prasko\a, CSc. Supervisor's e-mail address: Zuzana.Praskova^nifl.cimi.c/, Abstract: This thesis deals with detection of changes in the mean value (location) of a sequence of normally...
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Decomposition methods for time series with irregular observations
Hanzák, Tomáš ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
This work deals with extensions of classical exponential smoothing type methods for univariate time series with irregular observations. Extensions of simple exponential smoothing, Holt method, Holt-Winters method and double exponential smoothing which have been developed in past are presented. An alternative method to Wright's modification of simple exponential smoothing for irregular data, based on the corresponding ARIMA process, is suggested. Exponential smoothing of order m for irregular data as a generalization of simple and double exponential smoothing is derived. A similar method using a DLS (discounted least squares) estimation of polynomial trend of order m is derived as well. In all cases the recursive character of these methods is preserved making them easy to implement and high computationally effective. A program in which most of the methods presented here are available is a part of the work. Some numerical examples of their application are also included.
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Higher - order Markov chains and applications in econometrics
Straňáková, Alena ; Prášková, Zuzana (advisor) ; Sladký, Karel (referee)
In this paper, we generalize Raftery's model of Markov chain to a higher-order multivariate Markov chain model. This model is more suitable for practical applications because of smaller number of independent parameters. We propose a method of estimation of parameters of the model and apply it to the Credit risk measuring of a portfolio. We compute Value at Risk and Expected Shortfall in this portfolio. Theoretical results are applied to real data.
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Proposal for Insolvency Act ammendments in order to establish equality status of creditors in the process of personal banktruptcy through debts charge off
Prasková, Zuzana ; Smolík, Petr (advisor) ; Zoulík, František (referee)
Title: Proposal for Insolvency Act amendments in order to establish equality status of creditors in the process od personal bankruptcy through debts charge off Thesis summary: The purpose of my thesis is to describe the new form of personal bankruptcy through debts charge off and point out some weaknesses of the current legislation together with some proposals how to deal with them. The reasons that led me to choose this topic are i) new legislation of Insolvency Act which is effective from January 1st 2008, and ii) my practical experience with insolvency proceedings. The thesis composes from eleven chapters where each of them deals with particular phase of the process. Prior to the chapters there is an Introduction which describes the aim of the thesis, reasons for this specific topic and explanations of basic legislation related to personal bankruptcy. Chapter One focuses on origination of the insolvency law in the territory of The Czech Republic and is divided into three subchapters. The first subchapter focuses on the development of insolvency law before the origination of Czechoslovakia, the second subchapter describes changes in the insolvency law from 1918 and the last subchapter deals with the former Bankruptcy Act. Chapter Two clarifies basic changes that were introduced by the Insolvency Act and...
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Econometric systems of simultaneous equations in life insurance
Hendrych, Radek ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
In present work we deal with theoretical and practical issues related to econometric systems of (linear) simultaneous equations. In the first chapter we introduce to theoretical aspects of this problem. We devote considerable space to estimation procedures and comparisons of their properties, mention questions of identification, an inconsistency of OLS-estimates for the simultaneous modeling, tests of hypotheses specific to this area, dynamic systems and constructions of forecasts in models. In the second chapter we introduce selected basic concepts relevant to life insurance. In the third chapter we show the practical application of theoretical knowledge in the event of an econometric model of financial flows in the life insurance company operating on the Czech market. We compare ordinary estimation procedures (2SLS and 3SLS approach), perform some tests, which serve us to verify selected information on the studied model. We show the possibility of using residual bootstrap, including examples of use in the construction of confidence intervals. Finally we analyze several predictions of the estimated model of the life insurance company for predetermined scenarios for the development of selected variables, which is very important from practical point of view.
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