Naslov
Functional limit theorems for weakly dependent regularly varying time series

Autori
Krizmanić, Danijel

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Prirodoslovno matematički fakultet - Matematički odjel

Mjesto
Zagreb

Datum
12.10

Godina
2010

Stranica
157

Mentor
Basrak, Bojan

Ključne riječi
regular variation ; vague convergence ; point process ; Skorohod topology ; functional limit theorem

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA