Question A1. Consider the simple AR(1) model including a constant: 3'; = P1K1+o+: t=1,2,...,T We will call this Mode}: Model A. The OLS estimator for the autoregressive coefcient in model A is given by {51 = 23;; (14-1 (a 2:2 mm: - (a 212m) 2:2(1'31 - ( ELK1))? a Part (1): TRUE or FALSE model A is a dynamic model? a Part (ii): Show that we can rewrite the estimator as: A = 2:21:14 (a 22:2 Keno/2 is 2:21; 2:; 1411\": an: 101 - 231:2 (Ytl (% 2:2 Yt1))2 2:2 1121 1121 When the sample covariance between 1'}, and Yg_1_ is equal to 0, what must always be true about our estimate l? Why? I Part (iii): The estimator for the intercept, [30, is ven by 5'0. Derive the OLS estimator for the intercept in model A. a Part (iv): TRUE or FALE when the estimator for pl, ,61, is unbiased the OLS estimator for the intercept, 130, is also unbiased? Now consider the alternative model, Model B, given below: K = mK1+o+1X+u t=1,2,...,T And the estimated model: A. Y; = 0.84Yp,_1 - 0.21 + 12.37X t: 1,2, . . . ,T 0 Part (v): Calculate the long run coefcients for 30 and ,61 using the estimates above. How do they compare to the short run coefcients? Why? I Part (vi): The Mean Squared Prediction errors for the two models and Variance of the sum of the two squared prediction errors are given below: MSPEA = 226.4 MSPEB 181.1 Vl(:+1,A)2+(e+1,Bl2l = 529-4 Use the Diebold-Mariano statistic to evaluate the forecast. State clearly your null hypothesis, your alternative hypothesis, your decision rule and your decision