|
| |
|
|
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)
|
|
|
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
|
|
|
Interest Rate Risk Analysis by Principal Component Method
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Prášková, Zuzana (referee)
Presented study analyzes interest rate risk associated with the possession of given fixed coupon bond. In the first chapter, we define some of the basic concepts and provide description of available data. These are historical data on spot interest rates of zero-coupon bonds for various times to maturity which will be used for the construction of the yield curves. Based on these bond yield curves we evaluate the bond, thus obtaining a picture of the evolution of its price. Later on, we try to estimate its price tomorrow. We present two approaches how to deal with this problem. First approach is the normal interest rate risk analysis based on duration and convexity, second approach is the method of principal components which will be applied to the historical daily changes in yield curves. The method of principal components is introduced in detail.
|
|
|
Holt-Winters method for exponential smoothing
Koritarová, Lenka ; Cipra, Tomáš (advisor) ; Prášková, Zuzana (referee)
"his thesis de-ls with the methods of exponenti-l smoothingF et (rst the prin iE ples of exponenti-l smoothing -re expl-inedF e fo us on -si -ppro- hesX sinE gleD dou le smoothing -nd the rolt¡s methodF "hese pro edures -re suit- le for the modeling time series without se-son-l omponentF rowever in pr- ti e there -re frequent time series with se-son-lityF por su h time series the roltE inter¡s method is usedF "his method is -sed just on the prin iples of exponenti-l smooE thingF sn the l-st p-rt of this thesisD there is demonstr-ted using this methods on re-l d-t-F
|
|
| |
|
|
Tests for time series linearity
Melicherčík, Martin ; Prášková, Zuzana (advisor) ; Hendrych, Radek (referee)
Title: Testing for linearity in time series Author: Martin Melicherčík Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Zuzana Prášková, CSc., Department of Probability and Mathematical Statistics Abstract: In the first part of the thesis, a necessary theoretical base from time series analysis is explained, which is consequently used to formulate several tests for linearity. According to variety of approaches the theory includes wide range of knowledge from correlation and spectral analysis and introduces some basic nonlinear models. In the second part, linearity tests are described, classified and compared both theoretically and practically on simulated data from several linear and nonlinear models. At the end, some scripts and hints in R language are introduced that could be used when applying tests to real data. Keywords: linear time series, bispectrum, testing for linearity, nonlinear models
|
|
|
Models of integer-valued time series
Jarešová, Lucia ; Prášková, Zuzana (advisor) ; Vaněček, Pavel (referee)
In the presented work the generalized integer valued processes GINAR founded on the Steutel and van Harn generalized operator are studied. Properties of this operator, which are based on the sum of i.i.d. random variables are investigated including the determination of the domain of the operator and suggestion of possible construction of this operator. The attention is given on a weak stationary GINAR(p), the main properties of this process are described and it is shown that this process has an AR(p) representation, where the white noise consists of martingale differences. Further, the parameter estimators are described and consequently tested on extensive simulation with differently distributed innovations. The results are compared according to MSE. The work also contains a real data application. At the end the vector processes VGINAR are mentioned, that can also have a VAR representation. The functions for the program environment R are included.
|
|
|
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.
|
|
| |
guest ::
RSS feed.