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.
Represent this model in the state space form.
State the recursive relations for the Kalman …lter.
State the recursive relations for the Kalman smoother.
(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).
