Kalman Filter analysis

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Kilpailun tehtävänanto

I would like use the Kalman filter (not smoother) to estimate smooth values - in real-time - (for the position (Pt) and "velocity" (Vt, first derivative) of the attached time series.

This time series shows clear signs of mean reversion around zero, meaning that the acceleration (At, second derivative) should have a negative coefficient with Pt.

I would prefer a R-based solution, preferably using the FKF package.

I tried the following transition equation, unsuccessfully.

P(t+1)=(1 1 0.5 ) P(t) + Noise(P)
V(t+1)=(0 1 1 ) V(t) + Noise(V)
A(t+1)=(-Z 0 1) A(t) + Noise(A)

Additionally, I would like noises to be estimated (and not inputted).

As a newbie in Kalman filter, I’ve been struggling with this, but for someone who’s familiar with R and the Kalman filter, it should be an easy task.

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