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Functional limit theorems for weakly dependent regularly varying time series (CROSBI ID 377582)

Ocjenski rad | doktorska disertacija

Krizmanić, Danijel Functional limit theorems for weakly dependent regularly varying time series / Basrak, Bojan (mentor); Zagreb, Prirodoslovno-matematički fakultet, Zagreb, . 2010

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.

obranjeno

Podaci o ustanovi koja je dodijelila akademski stupanj

Prirodoslovno-matematički fakultet, Zagreb

Zagreb

Povezanost rada

Matematika