Speaker: Yunhong Lyu
Title: On Generalized Exponential Ornstein-Uhlenbeck processes with change-point
Abstract: In this talk, we introduce a novel stochastic process which is suitable for modeling positive datasets which exhibit periodic mean-reverting behavior. In particular, the proposed process is so-called generalized exponential Ornstein-Uhlenbeck (GEOU) process, and this is efficient for modeling financial datasets. We also consider an inference problem concerning the drift parameter of the proposed GEOU in the contexts of uncertain restriction along with a possible change-point. As opposed to similar methods in recent literature, the dimensions of the drift parameter are unknown and, we weaken some assumptions underlying the asymptotic properties of some estimators of the drift parameter. Further, we derive the unrestricted maximum likelihood estimator, the restricted maximum likelihood estimator and shrinkage estimators for the drift parameters as well an asymptotic test for testing the possible restriction. We also derive the asymptotic power of the proposed test and we establish the relative efficiency of the proposed estimators. Finally, we present the simulation results which corroborate the theoretical findings and we analyze a financial market data set. Beyond such interesting contributions, the additional novelty of our findings consist in the fact that we overcome the difficulties induced by the randomness fact of the proposed estimators.
Yunhong Lyu (a PhD candidate in Statisics under Dr. S. Nkurunziza) in the Department of Mathematics and Statistics at University of Windsor.
When? Thurs. April 6 at 3:00pm
Where? Lambton 9-118
Counts toward seminar attendance for MSc and PhD students in Math & Stats