Statistical State-Space Modeling via Kalman Filtration

Abstrakt

We start with a brief review of the theory underlying the Kalman filter (KF) statistical modeling based on the state-space approach. We will stress the prediction error decomposition as a highly effective way of computing the likelihood function, useful when maximum likelihood estimate of certain structural parameters is attempted. Next, we will illustrate how the state-space modeling and KF can be useful for solving practical problems from interesting real-life applications. Firstly, the state-space approach and KF estimation will be shown as a tool for estimation of time-varying parameters describing radon concentrations in houses, based on two underlying differential equations summarizing the radon and tracer dynamics. Secondly, we will show how the Kalman filtration can be useful for estimation of underlying growth curve of small children. Further, we will consider also multivariate approach useful for individualized natural gas consumption modeling.