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Nonlinear continuous time modeling approaches in panel research
Author(s) -
Singer Hermann
Publication year - 2008
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2007.00373.x
Subject(s) - extended kalman filter , mathematics , kalman filter , control theory (sociology) , nonlinear filter , filter (signal processing) , nonlinear system , invariant extended kalman filter , linearization , stochastic differential equation , filtering problem , alpha beta filter , ensemble kalman filter , interval (graph theory) , discrete time and continuous time , computer science , filter design , statistics , moving horizon estimation , artificial intelligence , physics , control (management) , quantum mechanics , combinatorics , computer vision
Stochastic differential equations (SDE) are used as dynamical models for cross‐sectional discrete time measurements (panel data). Thus causal effects are formulated on a fundamental infinitesimal time scale. Cumulated causal effects over the measurement interval can be expressed in terms of fundamental effects which are independent of the chosen sampling intervals (e.g. weekly, monthly, annually). The nonlinear continuous–discrete filter is the key tool in deriving a recursive sequence of time and measurement updates. Several approximation methods including the extended Kalman filter (EKF), higher order nonlinear filters (HNF), the local linearization filter (LLF), the unscented Kalman filter (UKF), the Gauss–Hermite filter (GHF) and generalizations (GGHF), as well as simulated filters (functional integral filter FIF) are compared.