The state space representation is a flexible technique originally developed in automatic control engineering to represent, model, and control dynamic systems. Thereby the unobserved or partially observed state of a system in period t is summarized by an m-dimensional vector \(X_t\) . The evolution of the state is then described by a VAR model of order one usually called the state equation. A second equation describes the connection between the state and the observations given by a n-dimensional vector \(Y_t\) . Despite its simple structure, state space models encompass a large variety of model classes: VARMA, respectively, VARIMA models (VARIMA models stand for vector autoregressive integrated moving-average models); unobserved-component models; factor models; structural time series models that decompose a given time series into a trend, a seasonal, and a cyclical component; models with measurement errors; VAR models with time-varying parameters, etc. See the examples given in Sect. 17.2.