Introduction to Local Level Model and Kalman Filter

Local Level Model
General framework
yt = µt + εt, εt ∼ N ID(0, σ 2 ε)
µt+1 = µt + ηt, ηt ∼ N ID(0, σ 2 η),
µ1 ∼ N (a, P)
◮ The level µt and the irregular εt are unobservables;
◮ Parameters: σ 2 ε and σ 2 η;
◮ Trivial special cases:
◮ σ 2 η = 0 =⇒ yt ∼ N ID(µ1, σ 2 ε) (WN with constant level);
◮ σ 2 ε = 0 =⇒ yt+1 = yt + ηt (pure RW);
◮ Local Level is a model representation for EWMA forecasting.