Understanding state-space models
In this chapter, you will see references to state-space models. In Chapter 10, Building Univariate Time Series Models Using Statistical Methods, you were introduced to exponential smoothing (Holt-Winters) and ARIMA-type models. Before defining what state-space models are, I want to point out that these models can be represented in a state-space formulation.
State-Space Models (SSM) have their roots in the field of engineering (more specifically control engineering) and offer a generic approach to modeling dynamic systems and how they evolve over time. In addition, SSMs are widely used in other fields, such as economics, neuroscience, electrical engineering, and other disciplines.
In time series data, the central idea behind SSMs is that of latent variables, also called states, which are continuous and sequential through the time-space domain. For example, in a univariate time series, we have a response variable at time 
; this is the observed...
