Abstract
ABSTRACTWe study the existence and properties of stationary solution of ARCH-type equation , where are standardized i.i.d. random variables and the conditional variance satisfies an AR(1) equation with a Lipschitz function and real parameters . The paper extends the model and the results in Doukhan, Grublytė, and Surgailis [A nonlinear model for long memory conditional heteroscedasticity. Lithuanian Math J. 2016;56:164–188] from the case to the case . We also obtain a new condition for the existence of higher moments of which does not include the Rosenthal constant. In the particular case when Q is the square root of a quadratic polynomial, we prove that can exhibit a leverage effect and long memory. We also present simulated trajectories and histograms of marginal density of for different values of γ.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
