2. (20 pts) Suppose that simple return of a monthly stock index follows an AR dynamics, xt = 0.01 + t + 0.2Xt-1, where Et ~ i.i.d. N(0,1). ~ a) What is the mean of the simple return of this monthly stock? b) What is the variance of the simple return of this monthly stock? c) Consider the forecast origin h 100 with x 100 = 0, X99 = -0.2, X98 0.4. Compute the 1-step-ahead forecast of the simple return at the forecast origin h = 100. d) Provide two features of AR models. 2. (20 pts) Suppose that simple return of a monthly stock index follows an AR dynamics, xt = 0.01 + t + 0.2Xt-1, where Et ~ i.i.d. N(0,1). ~ a) What is the mean of the simple return of this monthly stock? b) What is the variance of the simple return of this monthly stock? c) Consider the forecast origin h 100 with x 100 = 0, X99 = -0.2, X98 0.4. Compute the 1-step-ahead forecast of the simple return at the forecast origin h = 100. d) Provide two features of AR models