Functional limit theorems for weakly dependent regularly varying time series (CROSBI ID 377582)
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Podaci o odgovornosti
Krizmanić, Danijel
Basrak, Bojan
engleski
Functional limit theorems for weakly dependent regularly varying time series
This thesis investigate the asymptotic distributional behavior of the partial sum stochastic process of a strictly stationary sequence of random variables, under the properties of weak dependence and regular variation. The main result of this thesis gives conditions under which a strictly stationary, regularly varying sequence of random variables with index between 0 and 2 satisfies the functional limit theorem with respect to the Skorohod's M1 tolology, with the limit being a stable Levy process, which is characterized in terms of its characteristic triple. We also investigate conditions under which four examples of time series models, namely moving average, GARCH, ARMA and stochastic volatility models, satisfy the functional limit theorem.
regular variation ; vague convergence ; point process ; Skorohod topology ; functional limit theorem
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Podaci o izdanju
157
12.10.2010.
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Prirodoslovno-matematički fakultet, Zagreb
Zagreb