Introduction to Local Level Model and Kalman Filter
Introduction to Local Level Model and Kalman Filter
Introduction to Local Level Model and Kalman Filter
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<strong>Kalman</strong> <strong>Filter</strong><br />
The unobserved variable µt can be estimated from the<br />
observations with the <strong>Kalman</strong> filter:<br />
vt = yt − at,<br />
Ft = Pt + σ 2 ε,<br />
Kt = PtF −1<br />
t ,<br />
at+1 = at + Ktvt,<br />
Pt+1 = Pt + σ 2 η − K 2 t Ft,<br />
for t = 1, . . . , n <strong>and</strong> starting with given values for a1 <strong>and</strong> P1.<br />
◮ Writing Yt = {y1, . . . , yt}, define<br />
at+1 = E(µt+1|Yt), Pt+1 = var(µt+1|Yt).
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