ARMA Exam Q

Question 1

ACF and PACF behaviour for an MA(q)

Answer 1

• an MA(q) model typically has an ACF that drops off after q lags, while its PACF decays gradually

Question 2

ACF and PACF behaviour of an AR(p) model

Answer 2

• an AR(p) model typically has a PACF that drops off after p lags, while its ACF decays gradually

Question 3

Why are ACF and PACF useful?

Answer 3

• helps in selecting the appropriate order of the AR/MA model and avoids over/underfitting the model

Question 4

Covariance formula

Answer 4

Cov(X,Y) = E[(X - E[X])(Y - E[Y])]

Question 5

Variance formula

Answer 5

Var(X) = E[X²] - (E[X])²

Question 6

Why are MA processes always stationary?

Answer 6

• they are finite linear combinations of independent, identically distributed noise terms.

Question 7

Autocorrelation formula

Answer 7

p_k = γ_k / γ₀
- γ_k = Cov(y_t,y_t-k)
- γ₀ = Var(y_t)