Mathematics, 25.02.2020 23:59 ili28
If {xt } is stationary with E [xt] = 0 and corr(xt , xt −1) = rho1, show that the best linear predictor of xt based on xt −1 is rho1xt −1. (You will need to use calculus to do this problem. Here are some hints. First, define the random variables Y = xt , X = xt −1. Consider any linear predictor Yˆ = a + bX , where a and b are any numbers. Consider the mean squared forecasting error, MSE = E [Y − Yˆ] 2 = E [Y − (a + bX )]2.
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If {xt } is stationary with E [xt] = 0 and corr(xt , xt −1) = rho1, show that the best linear predic...
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