(a) Explain the link between state space models and the Kalman filter

(b) What is the difference between the Kalman filter and the Kalman smoother?

(c) In the context of a state space model, how can we determine whether allowing the parameters to vary over time is necessary?

(d) Suppose that we wish to estimate a CAPM-style model for fund manager performance where both the Jensen’s alpha and the market beta vary over time. Using equations, describe the model that we would estimate

(e) If the Kalman filter is implemented using a set of recursive formulae, why is it still necessary to use maximum likelihood estimation?