Question 2 (20 points) An AR(2) process is defined by where e, is an i.i.d. process with mean 0 and variance o'. An MA (2) process is defined by Y, = 0.1 + 0.2 1 + 0.36, 2 + et. where e is an ii.d. process with mean 0 and variance o'. This question will compare and contrast these two processes. (a) Show that the AR(2) process is weakly stationary and find the uncondi- (5) tional mean of X. Find the conditional means of Xi, and X142 given the information set Ix, = (Xt, X_1: X, 2. ...] on day t. 774N1: Advanced Financial Modelling (b) Compute the autocorrelations of the AR(2) process: P1 = corr(X, Xi_1) (5) and py = corr(X, X-2). (c) Show that the MA(2) model is weakly stationary and find the unconditional (5) mean of Yr. Find the conditional means of You and Vi42 given the informa- tion set lyr = {Yi, Yi_1, Y 2, -..} on day t. (d) Compute the autocorrelations of the MA (2) model: p1 = corr(Yt, Yi_1) and (5) p2 = corr (Yi, Yi-2)