Consider the IMA(0, 1, 1) model (1 − ????)???????? = (1 − ????)????????, where the ???????? are i.i.d.

N(0, ????2

????).

(a) Derive the expected value and variance of ????????, ???? = 1, 2, … , assuming that the process starts at time ???? = 1 with ????0 = 10.

(b) Derive the correlation coefficient ???????? between ???????? and ????????−????, conditioning on ????0 =

10. Assume that ???? is much larger than the lag ????.

(c) Provide an approximate value for the autocorrelation coefficient ???????? derived in part (c).