Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms

Continuous time models with sampled data possess several advantages over conventional discrete time series and panel models (cf., e.g. special issue Stat. Neerl. 62(1), 2008). For example, data with unequal time intervals between the waves can be treated efficiently, since the model parameters of the dynamical system model are not affected by the measurement process. The continuous-discrete state space model is a combination of continuous time dynamics (stochastic differential equations, SDE) and discrete time noisy measurements. Maximum likelihood (ML) estimation of linear panel models is discussed using Kalman filtering and structural equations models (SEM). Pure time series and correlated panel data (e. g. with random time effects) can be treated exactly by SEM methods. Nonlinear panel models are estimated by approximate filtering methods such as the extended Kalman filter (EKF), the local linearization filter (LLF), the Gauss-Hermite filter (GHF) and the unscented Kalman filter (UKF). Again, correlated panels are treated by stacking the panel units in a vector Ito equation. Finally, spatial dynamical models are discussed. The state variables are random fields given as solutions of stochastic partial differential equations (SPDE), driven by a space-time white noise. Furthermore, the fields are filtered and estimated with noisy and sampled measurements.