In Example 6.8, fit a true series evolving according to an RW(3) model such that

\[\theta_{t}=3 \theta_{t-1}-3 \theta_{t-2}+\theta_{t-3}+\omega_{t}\]

and assess fit against the RW(2) model.

Data from Example 6.8

Transcribed Image Text:

This example illustrates the detection of a signal in noisy data when the form of the signal is known. Thus consider a simulated series generated to follow the truncated and asymmetric form (for t = 1, ...,200) with true signal y = 0 + ~ N(0, 1) 0 = (12/) exp(-[t- 130]/2000). The maximum value of the true series is just under 4 at t = 130, with the true series being effectively zero for t < 50.