1. (6 points) Consider the model ytyt=yt+t=+1yt1+t+t1 for t=1,,n, where yt is the observed time series and is an unknown constant. The disturbances tN(0,2) and tN(0,2) are mutually and serially independent at all times and lags. Assume {yt} is stationary. (a) Represent this model in the state space form. (b) State the recursive relations for the Kalman filter. (c) State the recursive relations for the Kalman smoother. 1. (6 points) Consider the model ytyt=yt+t=+1yt1+t+t1 for t=1,,n, where yt is the observed time series and is an unknown constant. The disturbances tN(0,2) and tN(0,2) are mutually and serially independent at all times and lags. Assume {yt} is stationary. (a) Represent this model in the state space form. (b) State the recursive relations for the Kalman filter. (c) State the recursive relations for the Kalman smoother