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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Differential equations and stability of competitive economy
 Šabata, Marek ; Bárta, Tomáš (advisor) ; Adam, Tomáš (referee)
In the thesis, the author will analyse the theory of differential equations and its applications in economic model of price adjustment processes in competitive markets. First of all, the economic model sufficient to study stability of the market is introduced. Next microeconomic theory of competitive markets is presented and theory of differential equations is laid out, including the stability theory. Differences between the general model and the pure exchange model are discussed. Under certain microeconomic assumptions such as weak axiom of revealed preferences, gross substitutability, Walras's law and other properties of competitive markets, local and global stability of the market is proved. Powered by TCPDF (www.tcpdf.org)
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Nonlinear ARMA model
 Šabata, Marek ; Lachout, Petr (advisor) ; Prášková, Zuzana (referee)
The thesis regards theory of nonlinear ARMA models and its application on financial mar- kets data. First of all, we present general framework of time series modeling. Afterwards the theory of linear ARMA models is layed out, since it plays a key role in the theory of nonlinear models as well. The nonlinear models presented are threshold autoregressive model (TAR), autoregressive conditional heteroscedastic model (ARCH) and generalized autoregressive conditional heteroscedastic model (GARCH). For each model, we derive a method for esti- mating the model's parameters, asymptotic properties of the estimators and consequently confidence regions and intervals for testing hypotheses about the parameters. The theory is then applied on financial data, speficically on the data from Standard and Poor's 500 index (S&P500). All models are implemented in statistical software R. 1
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See also: similar author names
2 Šabata, Martin
2 Šabata, Milan
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