Consider the ARIMA model xt = wt + wt2. (a) Identify the model using the notation ARIMA(p, d, q) (P, D, Q)s. (b) Show

Consider the ARIMA model xt = wt + Θwt−2.

(a) Identify the model using the notation ARIMA(p,

d, q) × (P, D, Q)s.

(b) Show that the series is invertible for |Θ| < 1, and find the coefficients in the representation wt =

Õ∞

k=0

πk xt−k .

(c) Develop equations for the m-step ahead forecast, x˜n+m, and its variance based on the infinite past, xn, xn−1, . . . .