Suppose a process {Y{} is composed of two (unobservable) components, Y= P4+et, where P, is the "permanent component and e4 the transitory component of Yt. Let {P{} satisfy a random walk model P = P-1+at, where at are independent random variables with E(at) = 0 and Var(at) = 0, and let the et be independent random variables with E(et) = 0, Var(et) = d, with {at} and {e} independent. (a) Show that the process W4 = Y; Y41 has ACF of the form of an MA(1) process, and hence {Y{} is an IMA(0,1,1) process satisfying Yt =Yt-1 + Et - 65t-1, where the Et are independent with E (et) = 0 and Var(et) = 02. (b) Give explicit expressions for the parameters and oin terms of oa and by equating two equivalent expressions for the autocovariances (0) and 7(1) of the process {W}. (C) In particular, if c = 1.8 and 02 = 2.5, determine values of 0 and o2 in the IMA(0,1,1) model for {Yt}. Suppose a process {Y{} is composed of two (unobservable) components, Y= P4+et, where P, is the "permanent component and e4 the transitory component of Yt. Let {P{} satisfy a random walk model P = P-1+at, where at are independent random variables with E(at) = 0 and Var(at) = 0, and let the et be independent random variables with E(et) = 0, Var(et) = d, with {at} and {e} independent. (a) Show that the process W4 = Y; Y41 has ACF of the form of an MA(1) process, and hence {Y{} is an IMA(0,1,1) process satisfying Yt =Yt-1 + Et - 65t-1, where the Et are independent with E (et) = 0 and Var(et) = 02. (b) Give explicit expressions for the parameters and oin terms of oa and by equating two equivalent expressions for the autocovariances (0) and 7(1) of the process {W}. (C) In particular, if c = 1.8 and 02 = 2.5, determine values of 0 and o2 in the IMA(0,1,1) model for {Yt}