This book provides a comprehensive approach to the many computational procedures that can be applied to a previously specified linear model in State-Space (here-after, SS) form. Our interest in this field is motivated by the important advantages of the SS approach. Some of them are:

Any linear time series model can be written in an equivalent SS form 1 . In particular, ARIMAX, VARMAX or transfer functions can be represented in this way, see Subsection 2.2.4. In other cases, such as that of structural time series models (see Harvey [118]) the model is directly defined in SS form, so no translation is required.

Conversely, any linear SS model can be written in an equivalent VARMAX form, see Chapter 9.

The flexibility of the SS representation allows one to accommodate nonstandard situations like time-varying parameters (Pagan [173] and Watson and Engle [219]), unobserved variables (Harvey [118]), observation errors (Terceiro [206]), aggregation constraints (Casals, Sotoca and Jerez [46]) or missing in-sample values (Ansley and Kohn [7], Kohn and Ansley [137] and Naranjo, Trindade and Casella [165]).

System engineering provides a wealth of excellent “off-the-shelf” procedures and ideas to solve many relevant problems such as the specification, estimation and optimal control of SS models.