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Change detection in RCA models
Biolek, Jiří ; Prášková, Zuzana (advisor) ; Hudecová, Šárka (referee)
The thesis describes Random Coefficient Autoregressive time series mo- dels (RCA models). In first chapter we introduce different types of estimati- ons for coefficients of RCA model. Main part is in second chapter, where we describe detection changes procedures for all methods mentioned in chapter one, here the thesis expands the current theory about change detection of wei- ghted least square method and functional estimation. In last chapter we sum- marize results of simulation study. 1
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Kernel estimates of hazard function
Selingerová, Iveta ; Horová, Ivanka (advisor) ; Prášková, Zuzana (referee)
Kernel estimates of hazard function Abstract This doctoral dissertation is devoted to methods for analysis of censored data in survival analysis. The main attention is focused on the hazard function that reflects the instantaneous probability of the event occurrence within the next time instant. The thesis introduces two approaches for a kernel esti- mation of this function. In practice, the hazard function can be affected by other variables. The most frequently used model suggested by D. R. Cox is presented and moreover two types of kernel estimates to estimate a condi- tional hazard function are proposed. For kernel estimates, there is derived some statistical properties and proposed methods of bandwidths selection. The part of the thesis is extensive simulation study where theoretical results are verified and the proposed methods are compared. The last chapter of the thesis is devoted to an analysis of real data sets obtained from different fields.
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Volatility modeling
Jurka, Vojtěch ; Prášková, Zuzana (advisor) ; Večeř, Jan (referee)
In the thesis we deal with modelling volatility conditional on past shocks. Traditional ARCH and GARCH models proposed by Engle(1982) and Bollerslev(1986) are investigated as well as several generalizations of GARCH model that capture asymmetric reaction on positive and negative excess returns, namely GJR-GARCH, TGARCH and EGARCH. Selected models are then applied to four commodities traded on Chicago Mercantile Exchange that represent various sectors of commodity market. Our first key finding is that in short horizon all considered models have similar performance, while in longer horizon, EGARCH and TGARCH give more precise results. The second is that, measured by an average percentage error, there is no significant difference in quality of predictions among selected assets across commodity sectors.
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Detection of instabilities in some panel data
Láf, Adam ; Hušková, Marie (advisor) ; Prášková, Zuzana (referee)
This thesis deals with the detection of change in the intercept in panel data re- gression model. We are interested in testing a null hypothesis that there was no change in the intercept during the observation period in case with no depen- dency between panels and with the number of panels and observations in each panel going to infinity. Based on the results for simplified case with no additional regressors we propose a statistical test and show its properties. We also derive a consistent estimate of the parameter of change based on the least squares me- thod. The main contribution of the thesis is the derivation of theoretical results of the proposed test while variances of errors are known and its modification for unknown variance parameters. A large simulation study is conducted to examine the results. Then we present an application to real data, particularly we use four factor CAPM model to detect change in monthly returns of US mutual funds during an observation period 2004-2011 and show a significant change during the sub-prime crisis in 2007-2008. This work expands existing results for de- tecting changes in the mean in panel data and offers many directions for further beneficial research. 1
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Applications of bootstrap methods to time series
Baumová, Tereza ; Prášková, Zuzana (advisor) ; Hlávka, Zdeněk (referee)
Práce se vìnuje studiu variant metody bootstrap vhodných pro vy¹etøování vlastností autoregresních procesù s náhodnými koe cienty. Ètenáø je nejprve se- známen s pùvodní metodou bootstrap navr¾enou pro nezávislé stejnì rozdìlené náhodné velièiny a se základními variantami této metody bì¾nì pou¾ívanými pro analýzu èasových øad. Poté je pøedstaven autoregresní proces s náhodnými koe - cienty øádu p (RCA(p)). Jsou popsány základní vlastnosti tohoto procesu a blí¾e prozkoumány vlastnosti procesu RCA(1). V dal¹í èásti jsou uvedeny varianty me- tody bootstrap, které jsou v pøípadì procesu RCA(1) konzistentní, a pro metodu wild bootstrap je odvozena konzistence pro proces RCA(2). V poslední kapitole jsou na simulovaných datech ovìøeny vlastnosti popsaných metod. 1
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Autoregressive models
Rathouský, Marek ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The purpose of this thesis is to compare the classic autoregressive model of order 1 to integer autoregressive model of order 1. Considering the popularity of AR(1) model, only the basics are covered within this thesis. The main focus is on the INAR(1) model. Operator ◦ necessary for INAR(1) definition is intro- duced alongside with its properties with proof. All of the non-trivial properties of INAR(1) are followed by detailed proof, stationarity condition is also derived. Common estimation techniques are described for poisson INAR(1) model. This thesis also contains simulation study, which focuses on the rate of convergence of estimates of parameters. 1
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Testing Structural Changes Using Ratio Type Statistics
Peštová, Barbora ; Hušková, Marie (advisor) ; Prášková, Zuzana (referee) ; Jarušková, Daniela (referee)
Testing Structural Changes Using Ratio Type Statistics Barbora Peštová Charles University in Prague, Faculty of Mathematics and Physics, Department of Probability and Mathematical Statistics, Czech Republic Abstract of the doctoral thesis We deal with sequences of observations that are naturally ordered in time and assume various underlying stochastic models. These models are parametric and some of the parameters are possibly subject to change at some unknown time point. The main goal of this thesis is to test whether such an unknown change has occurred or not. The core of the change point methods presented here is in ratio type statistics based on maxima of cumulative sums. Firstly, an overview of thesis' starting points is given. Then we focus on methods for detecting a gradual change in mean. Consequently, procedures for detection of an abrupt change in mean are generalized by considering a score function. We explore the possibility of applying the bootstrap methods for obtaining critical values, while disturbances of the change point model are considered as weakly dependent. Procedures for detection of changes in parameters of linear regression models are shown as well and a permutation version of the test is derived. Then, a related problem of testing a change in autoregression parameter is studied....
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Financial time series model identification
Fučík, Jan ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
This thesis deals with the financial time series model identification. The univariate and multivariate ARMA models and their identification criteria are described. The procedures using the correlation structure of the time series and some information criteria are presented. The functioning of the criteria is verified on simulated time series AR, MA and ARMA. Afterwards, the criteria are compared in terms of reliability and simplicity of use. Finally, there are two examples of univariate and multivariate ARMA model identification for the real financial time series. The data and the R programme source code are enclosed on a CD. Powered by TCPDF (www.tcpdf.org)
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Special problems of non-stationarity in financial time series
Radič, Pavol ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
The aim of this thesis is a detailed analysis of selected approaches of unit root testing. First chapter deals with the basic knowledge of the theory of stochastic processes. Further, we describe Dickey-Fuller tests, t-tests and likelihood ratio tests for the presence of a unit root and derive their asymptotic properties. Numerical studies include comparison of accuracy of the parameter estimates, estimating quantiles of the presented distributions, their graphical presentation and determination of power of our tests. The acquired theoretical knowledge is applied on real data which were analyzed using software Mathematica and R. Powered by TCPDF (www.tcpdf.org)
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