| Abstract [eng] |
The thesis introduces new nonlinear models with long memory which can be used for modelling of financial returns and statistical inference. Apart from long memory, these models are capable to exhibit other stylized facts such as asymmetry and leverage. The processes studied in the thesis are defined as stationary solutions of certain nonlinear stochastic difference equations involving a given i.i.d. “noise”. Apart from solvability issues of these equations which are not trivial by itself, it is proved that their solutions exhibit long memory properties. Finally, for a particularly tractable nonlinear parametric model with long memory (GQARCH) we prove consistency and asymptotic normality of quasi-ML estimators. |
