If {3:} is stationary with E[wt] : 0 and corr(act, $3-1) : p1, show that the best linear predictor of wt, based on xt_1 is placid. You will need to use calculus to do this problem. Here are some hints: First, dene the random variables Y = x: and X = xt_1. Consider any linear predictor 17' = a, + bX, where a. and b are any numbers. Consider the mean squared forecasting error, MSE = E[Y YE : E [Y (a + bX)]2. Take the derivative of MSE with respect to a and set it equal to zero. Similarly, take the derivative of MSE with respect to b and set it equal to zero. Let's assume that the solution to these two equations for a. and I) gives us the coefficients which minimize MSE. By solving these two equations, you should conclude that the best a and b are given by a = 0 and b = E[X Y] / Var [X]. Now, use the fact that {act} is stationary with EM] 2 0 to show that the above expression for b is the same is p1 in this case