State space models are introduced as a natural extension of linear time series models where the phenomena of interest are not observed directly, e.g. the phenomenon of interest is CO2 production, but the actual observed time series is CO2 concentration. The important concept of filtering is introduced and in particular, the Linear Kalman Filter is introduced and the resulting likelihood is given such that parameters can be estimated. The ARIMAX models presented in a previous chapter are given in state space form. The method is introduced using time series of CO2 production. The chapter is finalized using modelling of window position (open or closed) using a generalized state-space model based on the exponential family of distributions.