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Statistical State-Space Modeling via Kalman Filtration pp. 77-110 $100.00
Authors:  (Marek Brabec, Academy of Sciences of the Czech Republic, Institute of Computer Science, Department of Nonlinear Modeling, Praha, Czech Republic, and others)
Abstract:
In this paper, we will start with a brief review of the theory underlying the Kalman
filter (KF) applications in statistical modeling based on the state-space approach. In
particular, we will stress the prediction error decomposition (achievable through the KF
application to the analyzed time series) as a highly effective way of computing the
likelihood function, useful when maximum likelihood estimate (MLE) of certain
structural parameters is attempted. One-step prediction errors (evaluated at the MLE of
structural parameters) are useful for other purposes as well, including the model
diagnostics. Similarly, KF (evaluated at the MLE of structural parameters) is used to
estimate state variables.
Next, we will illustrate how the state-space modeling and KF can be useful for
solving practical problems from several interesting real-life applications.
Firstly, the state-space approach and subsequent (extended) KF estimation will be
shown as a valuable tool for estimation of time-varying parameters (radon entry rate and
air exchange rate) describing radon concentrations in houses. The model here will be
built on two underlying differential equations summarizing the radon and tracer
dynamics, similarly as in Brabec, Jilek (2007a). As such, the methodology can be viewed
as a flexible way to approach functional data analysis, Ramsay, Silverman (1997). 


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Statistical State-Space Modeling via Kalman Filtration pp. 77-110