(30 points) You consider two possible models for forecasting aggregate stock returns. Let Return, denote monthly returns on CRSP value- weighted index, that is, return =logPt-logPt- with At being the index level at time t. Let dive denote the dividend yield, i.e., the ratio of the dividend to the stock price at time t. The first model is an AR(2) model. The estimates are given by (standard errors are in parentheses) return, = 0.328-0.053return -1 + 0.053return; -2;R2 =0.0014. (0.199) (0.051) (0.048) The F statistic for the coefficients on the two lagged returns equals 0.968. The second model is an ADL(1,1) model: return, = 0.090 + 0.078return; -1 + 0.026/og(divt -1);R2 =0.0134. (0.039) (0.057) (0.012) 1. In the AR(2) model, are the two coefficients on the lagged returns jointly significant? Explain your answer. (Some relevant 5% critical values for the F distribution are F1. o = 3.84, F2, co = 3.00, F3. 0 = 2.60.) 2. In the ADL(1,1) model, is log(div-) statistically significant? What is the expected change in return, associated with a 1% increase in divt. ? Construct a 95% confidence interval for this change. 3. Use BIC to determine which model is a better forecasting model. 4. Should you interpret the coefficient of log(div-) as the causal effect of log(div_) on Return ?Explain your