511 – Statistical Applications in the Physical Sciences
Simulation Study of Time Series Models Generated by Underlying Dynamics
Alexander Gluhovsky
Purdue University
Evidence Matangi
Purdue University
Time series data are commonly handled via fitting traditional time series models, but finding adequate models for atmospheric series is often challenging due to inherently nonlinear data generating mechanisms and prohibitively short observed records. Classical time series approaches are well justified in areas, where data only are available. Atmospheric dynamics, by contrast, offers an important advantage in providing governing equations to address the flood of often-problematic data. Our research aims at incorporating this considerable and reliable part of the existing knowledge of atmospheric dynamics in the development of novel time series models. Specifically, the latter are developed as physically sound extensions of the celebrated Lorenz model (the so-called G-models), which is motivated by recent progress in statistical properties of dynamical systems. In particular, it has been proven that the Lorenz model flow possesses a physical ergodic invariant probability measure and satisfies the central limit theorem. In the talk, several G-models will be explored via simulations for the role of atmospheric time series models.