Question A2. Consider the simple AR(1) model including a constant: Y: = P1K1+50+-t t=1,2,...,T We will call this Model: Model A. The OLS estimator for the autoregressive coefcient in model A is given by ,1 = Siam14%;, 2:12 YHMY: ea 2:12 Y) 2;: (14-1 (a ELK1))? 0 Part (i): TRUE or FALSE model A is a nite distributed lag model? a Part (ii): Show that we can rewrite the estimator as: 2:2 (YH (a1: 23:2 mum - (Fl1 Sign = 3 2221411\": 2-117, 2:; (141 (171, 23;: 141))? T i; 122.1 Ya When the Y, and Yt_1 are always independent, what must always be true about our estimate 51? Why? i51= 0 Part (iii): The estimator for the intercept, g, is given by do. 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, ,80, is also unbiased? Now consider the alternative model, Model B, given below: 1\": = 911's-1+ [30 + [31X]: + H: t = 1, 2, .. . ,T And the following estimates Short Run Long Run p1 0.17 N/A ,80 ??? 25.?6 s, ??? 1.29 a Part (v): You are given the long run coefcients above and the value of pl. Calculate the short run ooe'icients for 130 and l using the estimates above. How do they compare to the long run coefcients? Why? a 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 = 134.7 MSPEB 96.2 V[(=+1,A)2+(+1,B)2] = 289.4 Use the Diebold-Mariano statistic to evaluate the forecast. State clearly your null hypothesis, your alternative hypothesis, your decision rule and your decision