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If {xt } is stationary with E [xt] = 0 and corr(xt , xt β1) = rho1, show that the best linear predictor of xt based on xt β1 is rho1xt β1. (You will need to use calculus to do this problem. Here are some hints. First, define the random variables Y = xt , X = xt β1. Consider any linear predictor YΛ = a + bX , where a and b are any numbers. Consider the mean squared forecasting error, MSE = E [Y β YΛ] 2 = E [Y β (a + bX )]2.
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If {xt } is stationary with E [xt] = 0 and corr(xt , xt β1) = rho1, show that the best linear predic...
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