Description
1. (6 points) Consider the model
yt = yt + “t;
yt = + 1yt 1 + t + t 1
for t = 1; : : : ; n, where yt is the observed time series and is an unknown constant. The disturbances “t N (0; 2“) and t N (0; 2) are mutually and serially independent at all times and lags. Assume fytg is stationary.
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Represent this model in the state space form.
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State the recursive relations for the Kalman …lter.
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State the recursive relations for the Kalman smoother.
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(4 points) Assume the local linear trend model for Boston’ monthly tempera-ture data uploaded in the class website. Plot the Kalman …lter and smoother for
the data (Use either Python or EViews; see https://www.statsmodels.org/stable/examples/notebo for the Python code).