State Space Models

Abstract

State space models may be regarded as generalizations of the models considered so far. They have been used extensively in system theory, the physical sciences, and engineering. The terminology is therefore largely from these fields. The general idea behind these models is that an observed (multiple) time series y ₁ ,…, y _T depends upon a possibly unobserved state z _t which is driven by a stochastic process. The relation between y _t and z _t is described by the observation or measurement equation

$$ y_t = H_t z_t + v_t , $$

(18.1.1)

where H _t is a matrix that may also depend on the period of time, t, and v _t is the observation error which is typically assumed to be a noise process.