Lecture 12 State Space models

Question 1

SPM

Answer 1

Measuring the unobservable state(prediction, filtering, smoothing)
Estimation of unknown parameters(MLE)
SPM offer a uniform approach to a wide range of models and techniques.

Question 2

Kalman Filter?

Answer 2

optimal recursive data processing algorithm
assumes that variables being estimated are time dependent
calculates mean and variance of the unobserved state
the current best time estimate is updated whenever a new observation is obtained

Question 3

Procedure SPM?

Answer 3

1) State vector propagation
2) Parameter covariance matrix propagation
3) Compute Kalman Gain
4) State vector update
5) Parameter covariance matrix update

Question 4

Initialising SPM or problems?

Answer 4

If you have no information set diagonal values of parameter covariance matrix high, filter will then give a high weight to the first measurement, Elements of mü, F, Q, R are predetermined
set the initial parameters to physically realistic values.

Question 5

Unobserved Components Model (UCM)

Answer 5

Each component in the model captures some important feature of the series dynamics. Components in the model have their own probability model. Probabilistic component models include meaningful deterministic pattern as special cases. UCM can be formulated as linear SSm. Enables the use of Kalman filter. yt = time varying mean + periodic/seasonal component + noise