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310 Chapter 8 State-Space Models<br />

Figure 8-11<br />

A simulated time<br />

series from the fitted<br />

model to the goal data.<br />

Figure 8-12<br />

A second simulated time<br />

series from the fitted<br />

model to the goal data.<br />

0 1 2 3 4 5 6<br />

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oo<br />

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o<br />

oo<br />

oo<br />

o<br />

ooo<br />

0 5 10 15 20 25 30 35 40 45 50<br />

(Here p(xt+1|y (t) ) is a probability density when αt+1|t<br />

one-step prediction density is<br />

> 0 and λt+1|t > −1.) The<br />

0.0 0.5 1.0 1.5 2.0<br />

o<br />

oooo<br />

p yt+1|y (t <br />

o<br />

ooo<br />

o<br />

o<br />

oo<br />

0<br />

e<br />

−∞<br />

xt+1yt+1+ln(−xt+1)+αt+1|t x−λt+1|t b(x)+At+1|t<br />

dxt+1<br />

o<br />

o<br />

(λt+1|t + 1)α λt+1|t +1<br />

t+1|t (yt+1 + αt+1|t) −λt+1|t −2 , yt+1 > 0<br />

ooooo<br />

o<br />

ooooo<br />

o<br />

oo<br />

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ooooooooooooooooooooooooooo<br />

0 5 10 15 20 25 30 35 40 45 50<br />

o

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