Lecture 5 Slides

Question 1

What is a State space model?

Answer 1

Generalisation that includes all models covered and more

2019 exam gives this model in question

Question 2

Partitioned Gaussian Density

Answer 2

If needed, will be provided on exam

Question 3

Overview of Kalman filtering

Answer 3

Question 4

Kalman filter on AR(1)

Answer 4

Question 5

Kalman filter steps

Answer 5

Question 6

ARMA model in state space form

Answer 6

(Won’t be asked to derive, pitt says it’s too difficult in Mar 7 107mins)

Question 7

Assuming stationarity what is long run mean of a GARCH model

Answer 7

Where y_t = σ_t ε_t

σ_t² = α₀ + sum(α_iy_t-i² + sum(β_jσ_t-j²

Crucially in long run noise term disappears