Problem 1: (20 points) Consider the time series process Yb, Y1, . . . dened by: n+1 : (1w),u+wY{g+et fort:0,1,..., Where 0 S w 1 and explain the intuition for your conjecture. c) (5 points) Suppose now that w 2 1 and YO is deterministically equal to ,u (hence Y0 has variance zero). Derive formulas for IE[Y1] and Var(Y1). d) (5 points) Again, suppose that w = 1 and Y0 is deterministically equal to ,u (hence YD has variance zero). Give a conjecture for formulas for IE[Y;] and Var(l/}) for t > 1 and explain the intuition for your conjecture