Nonlinear Continuous Time ModelingApproaches in Panel Research

Stochastic differential equations (SDE) are used as dynamical models forcross sectional discrete time measurements (panel data). Thus causal effectsare formulated on a fundamental infinitesimal time scale. Cumulated causaleffects over the measurement interval can be expressed in terms of the fundamentaleffects which are independent of the chosen sampling intervals (e.g.weekly, monthly, annually etc.). The nonlinear continuous-discrete filter is thekey 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 unscented Kalman filter (UKF), theGauss-Hermite filter (GHF) and generalizations (GGHF), as well as simulatedfilters (functional integral filter FIF) are compared....