Question: 3. (50 points) Two independent random walks (unit roots) RA and RB and two independent stationary processes SA and SB are generated by the following

3. (50 points) Two independent random walks (unit roots) RA and RB and two independent stationary processes SA and SB are generated by the following processes RA=RA. + RB=RB1+12 SC: = PASA:1 +232 SD = PSB+ve a) (25 points) Two series X and Z are generated as X =RAE+SC ZERB + SD Explain whether it is possible for Xi and Z to be ICO). Explain whether it is possible for (X - Z.) to be non-stationary Explain whether it is possible for (SC + SD) to be stationary (b) (25 points) Consider the following regression equations (1) RA = no + RA 1 + aoRB1+ut. (2) RAbo+b;SC + b3SD, +13 (3) Xt=00+cIZA+Z1 + X1 +13 Discuss the validity of the following statements 1) Var(u) = 0 and the R2 from equation (1) is unity 11) The R from equation (1) is always greater than the R from equation (2) l) Equation (2) is the best model as it contains stationary explanatory variables. Equation (3) is the best model as it contains all the dynamics

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