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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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Beveridge-Nelson decomposition and its applications
Masák, Štěpán ; Prášková, Zuzana (advisor) ; Lachout, Petr (referee)
In this work we deal with the Beveridge-Nelson decomposition of a linear process into a trend and a cyclical component. First, we generalize the decom- position for multidimensional linear process and then we use it to prove some of the limit theorems for the process and its special cases, processes VAR and VARMA. Further, we define the concept of cointegration and introduce the po- pular VEC model for cointegrated time series. Finally, we show a method how to deal with infinite sums appearing in calculation of the Beveridge-Nelson decom- position and apply it to real data. Then we compare the results of this method with approximations using partial sums.
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Treshold models for financial time series
Stacho, Michal ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
In modeling of financial time series is widely accepted ARCH model with conditional heteroscedasticity, but this model is not able to operate with other non-linearities such as leverage or asymmetry (the volume of revenue is different when the yield is positive or negative). Therefore, we work in this thesis with threshold models TAR, TARCH and DTARCH. These models have piecewise linear conditional mean and DTARCH model even piecewise linear conditional variance. The main utility of threshold models is further specified test of threshold nonlinearity, which is the base for comprehensively defined procedure of determining the type of model, including an estimate of all its parameters. At the end, the procedures introduced in this text are demonstrated using simulated and real data. Powered by TCPDF (www.tcpdf.org)
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Stability in Autoregressive Time Series Models
Dvořák, Marek ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee) ; Picek, Jan (referee)
The main subject of this thesis is a change point detection in stationary vector autoregressions. Various test statistics are proposed for the retrospective break point detection in the parameters of such models, in particular, the derivation of their asymptotic distribution under the null hypothesis of no change. Testing procedures are based on the maximum like- lihood principle and are derived under normality, nevertheless the asymptotic results are valid for broader class of distributions and involve also the models with certain form of dependence. Simulation studies document the quality of the results.
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Selected problems of financial time series modelling
Hendrych, Radek ; Cipra, Tomáš (advisor) ; Arlt, Josef (referee) ; Prášková, Zuzana (referee)
Title: Selected problems of financial time series modelling Author: Radek Hendrych Department: Department of Probability and Mathematical Statistics (DPMS) Supervisor: Prof. RNDr. Tomáš Cipra, DrSc., DPMS Abstract: The present dissertation thesis deals with selected problems of financial time series analysis. In particular, it focuses on two fundamental aspects of condi- tional heteroscedasticity modelling. The first part of the thesis introduces and discusses self-weighted recursive estimation algorithms for several classic univariate conditional heteroscedasticity models, namely for the ARCH, GARCH, RiskMetrics EWMA, and GJR-GARCH processes. Their numerical capabilities are demonstrated by Monte Carlo experiments and real data examples. The second part of the thesis proposes a novel approach to conditional covariance (correlation) modelling. The suggested modelling technique has been inspired by the essential idea of the multivariate orthogonal GARCH method. It is based on a suitable type of linear time-varying orthogonal transformation, which enables to employ the constant conditional correlation scheme. The correspond- ing model is implemented by using a nonlinear discrete-time state space representation. The proposed approach is compared with other commonly applied models. It demon- strates its...
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Linear and bilinear models for time series from economics and finance
Kotrbová, Anežka ; Zichová, Jitka (advisor) ; Prášková, Zuzana (referee)
This bachelor thesis deals with linear and bilinear models used for modelling time series data applicable in economy and finance. The thesis consists of a theoretical and a practical part. The theoretical part briefly describes ARMA and bilinear process, issues of linear model identification, estimation of the parameters and moment properties of ARMA(1, 1) a BL(1, 0, 1, 1). The typical characteristics of bilinear models and the quality of the estimated parameters are examined by the simulation study in software Mathematica 10. The acquired findings are applied in search for a suitable model for time series of share prices of the company ČEZ. Powered by TCPDF (www.tcpdf.org)
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Detekce změn v lineárních modelech a bootstrap
Čellár, Matúš ; Prášková, Zuzana (advisor) ; Hušková, Marie (referee)
This thesis discusses the changes in parameters of linear models and methods of their detection. It begins with a short introduction of the two basic types of change point detection procedures and bootstrap algorithms developed specifically to deal with dependent data. In the following chapter we focus on the location model - the simplest example of a linear model with a change in parameters. On this model we will illustrate a way of long-run variance estimation and implementation of selected bootstrap procedures. In the last chapter we show how to extend the applied methods to linear models with a change in parameters. We will compare the performance of change point tests based on asymptotic and bootstrap critical values through simulation studies in both our considered methods. The performance of selected long-run variance estimator will also be examined both for situations when the change in parameters occurs and when it does not. 1
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Ecological regression
Poul, Pavel ; Zvára, Karel (advisor) ; Prášková, Zuzana (referee)
Tato práce se zabývá problémem při analýze dat, který vzniká agre- gací veličin do jednotlivých soubor·, pro které známe pouze pr·měry p·vodních veličin a počty jednotek, ze kterých tento soubor vznikl. Jedná se o problém nedo- statečného množství informací, který zp·sobuje nepřesné stanovení vztah· mezi p·vodními veličinami. Tato práce si klade za cíl detailně seznámit čtenáře s dopa- dy agregace dat, představit jednotlivé možnosti přístupu k problému a představit takové modely a předpoklady, které povedou ke správnému stanovení vztah· me- zi p·vodními veličinami. Práce je zakončena praktickým použitím jednotlivých přístup· na reálných datech. Výpočty jsou prováděny v software R. 1
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Models of integer-valued time series
Vagaský, Ján ; Prášková, Zuzana (advisor) ; Jonáš, Petr (referee)
In this thesis models of integer-valued time series based on random sums of random variables are studied. We describe basic properties of a simple branching process, an INAR(1) process and a first- order binomial autoregresive process. We prove the Markov property of each of these processes and study conditions required for the processes to be weak-stationary. Using generating functions of random variables we derive moments and cumulants up to the fourth order for INAR(1) process and binomial AR(1) process. Powered by TCPDF (www.tcpdf.org)
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Methods for periodic and irregular time series
Hanzák, Tomáš ; Cipra, Tomáš (advisor) ; Arlt, Josef (referee) ; Prášková, Zuzana (referee)
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicity
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