
Smooth Transition Autoregressive Models
Khýr, Miroslav ; Zichová, Jitka (advisor)
The aim of this work is describing theory of smooth transition autoregressive models, namely LSTAR and ESTAR models. The essential part of the work is devoted to the derivation of tests for linearity against the alternative of the re levant nonlinear model. There is also shown how to estimate the parameters of these models along with the selection procedure between the LSTAR and the ESTAR model. A simulation study was carried out, which deals with the power of linearity tests. At the end of the thesis, we applied the theory to some real data and we estimated the appropriate model for their representation. 1


Smooth Transition Autoregressive Models
Khýr, Miroslav ; Zichová, Jitka (advisor) ; Cipra, Tomáš (referee)
The aim of this work is describing theory of smooth transition autoregressive models, namely LSTAR and ESTAR models. The essential part of the work is devoted to the derivation of tests for linearity against the alternative of the re levant nonlinear model. There is also shown how to estimate the parameters of these models along with the selection procedure between the LSTAR and the ESTAR model. A simulation study was carried out, which deals with the power of linearity tests. At the end of the thesis, we applied the theory to some real data and we estimated the appropriate model for their representation. 1


Dependence analysis of categorical data from banking
Khýr, Miroslav ; Zichová, Jitka (advisor) ; Mazurová, Lucie (referee)
Title: Dependence analysis of categorical data from banking Author: Miroslav Khýr Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema tical Statistics Abstract: The aim of this work is describing in detail the theory of the log  linear expansion and graphical models for random vectors with a discrete distribution. Such vector can be used for modeling categorical variables for example in a po pulation of borrowers by a bank . We show how to estimate the probability of an individual category. We use a log  likelihood function. Independence graph can represent conditional independence of discretely distributed random variables. Using this theory, especially using deviance as test statistics, we can examine whether same data correspond to the selected graphical model. At the end of this work we apply the described theory to real data and determine the graphical mo del best fitting the dependence structure in a database from banking. From this graph we can deduce which variables are dependent and which are independent. Keywords: Log  linear expansion, graphical model, log  likelihood function ,de viance.
