Introduction to Local Level Model and Kalman Filter

Parameters in Local Level Model
We recall the Local Level Model as
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 unknown µt’s can be estimated by prediction, filtering
and smoothing;
◮ The other parameters are given by the variances σ 2 ε and σ 2 η;
◮ We estimate these parameters by Maximum Likelihood;
◮ Parameters can be transformed : σ 2 ε = exp(ψε) and
σ 2 η = exp(ψη);
◮ Parameter vector ψ = (ψε , ψη) ′ .