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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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Prediction of Pedestrian Movement During The Egress Situation
Hrabák, Pavel ; Ticháček, O.
The report summarizes the up-to-now progress in the application of the recursive estimation on the prediction of the pedestrian movement during the egress or evacuation situation. For these purposes a simple decision-making model has been introduced taking into account only the forward and sideways movement of pedestrians. Based on this model, a test simulation has been developed in order to test the applicability of the estimation tool to the stated decision-making model. Two main approaches of the decision process incorporated in the simulation are discussed and a modified version of the original model is presented. The report contains a manual to the used Matlab scripts and functions. The codes of needed m-files are incorporated as well.
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Approximate Bayesian Recursive Estimation: On Approximation Errors
Kárný, Miroslav ; Dedecius, Kamil
Adaptive systems rely on recursive estimation of a firmly bounded complex- ity. As a rule, they have to use an approximation of the posterior proba- bility density function (pdf), which comprises unreduced information about the estimated parameter. In recursive setting, the latest approximate pdf is updated using the learnt system model and the newest data and then ap- proximated. The fact that approximation errors may accumulate over time course is mostly neglected in the estimator design and, at most, checked ex post. The paper inspects this problem.
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