Introduction to Local Level Model and Kalman Filter

Kalman Filter Derived
◮ Our best prediction of yt based on its past is at. When the
actual observation arrives, calculate the prediction error
vt = yt − at and its variance Ft = Pt + σ 2 ε.
◮ The best estimate of the state mean for the next period is
based on both the current estimate at and the new
information vt:
at+1 = at + Ktvt,
similarly for the variance:
◮ The Kalman gain
Pt+1 = Pt + σ 2 η − KtFtK ′ t.
Kt = PtF −1
t
is the optimal weighting matrix for the new evidence.
◮ You should be able to replicate the proof of the Kalman filter
for the Local Level Model (DK, Chapter 2).