Check the exercise attached. Only bid if you can answer!
4 Consider the IMA(0,1,1) model given by Zt − Zt−1 = (1 − θ)et, where et is white noise with variance σ 2 .
(a) Derive the expected value and variance of Zt, t ≥ 1, where we assume that the process starts at t = 1 with Z0 = 10.
(b) Derive the correlation coefficient ρk between Zt and Zt−k, conditioning on Z0 = 10. Without loss of generality, you may assume that t is much larger than k.
(c) Provide an approximate value for the autocorrelation ρk derived from part (c).
5. For an MA(2) model, find the largest possible values of |ρ(1)| and |ρ(2)|. For full points, justify your work.
check the photo
0 comments