Below are the questions;

1. Consider the MA(2) process It = Wt + Wt-1 + Wt-2, where we is a white noise process with mean 0 and variance 1. (a) Find the ACVF for It. (b) Find the predictors ; and z. (c) Suppose that we wish to predict x2 from 21 and Es. Find the best predictor of 12 of the form 12 = at1 + 4313, where a, and as are constants. (d) Suppose that we wish to predict as from , and 25. Find the best predictor of is of the form is = aid, + agrs, where a, and as are constants. (e) Find the mean squared prediction error (MSPE) for the predictor that you found in (d). 2. Consider the function y(h) defined by 1, h =0, y(h) = -0.5, h =12, and 0, otherwise. (a) Show that y is an ACVF by providing a stationary process z, that has y as its ACVF. (b) For the process It with ACVF y, find the predictor x3. (c) What is the MSPE for ~}