Linear Gaussian State Space Modeling

Abstract

Linear Gaussian state space modeling is treated in this chapter. The prediction, filtering and smoothing formulas in the standard Kalman filter are shown. Model identification or, computation of the likelihood of the model is also treated. Some of the well known state space models that are used in this book as well as state space modeling of missing observations and a state space model for unequally spaced time series are shown. The final section is a discussion of the information square root filter/smoother, that we use in linear Gaussian state space seasonal decomposition modeling in Chapter 9. Not necessarily linear - not necessarily Gaussian state space modeling is treated in Chapter 6. A variety of illustrative examples of linear state space modeling is shown in Chapter 7.