 State-space model (time series)

A state-space model separates a latent transition equation $S_t=F{S}_{t-1}+Z_t$ from an observation equation $Y_t=H{S}_t+W_t$. A complete specification includes the initial-state law and its relation to the noise sequences, not just the two equations. Linear second-order models specify covariance structure; Gaussian versions additionally prescribe joint Gaussian laws.