Recall the definition of a linear predictor. Define (h) as the best linear predictor of xt+h...

 

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Recall the definition of a linear predictor. Define (h) as the best linear predictor of xt+h given Xt, ...,X+h-1 (the best linear predictor is the one with the smallest expected squared error). Consider an AR(2) xi+1 P1xt + 42xt-1 + Wi+1,t 1,2,..., where w; is Gaussian noise with •.. mean 0 and variance 1. For the questions below, express your results as a function of P1, 42 and Xt, ..., Xt+h-1• a. Compute the value of (1). b. Compute the value of X(2). c. Compute the value of X(h) for h > 2. d. Define x:(h) as the best linear predictor of x-h given Xt, Xt-1, ... Xt-h+1• Use the results from Question 1 to briefly comment on T(h). You do not need to provide any equations. Recall the definition of a linear predictor. Define (h) as the best linear predictor of xt+h given Xt, ...,X+h-1 (the best linear predictor is the one with the smallest expected squared error). Consider an AR(2) xi+1 P1xt + 42xt-1 + Wi+1,t 1,2,..., where w; is Gaussian noise with •.. mean 0 and variance 1. For the questions below, express your results as a function of P1, 42 and Xt, ..., Xt+h-1• a. Compute the value of (1). b. Compute the value of X(2). c. Compute the value of X(h) for h > 2. d. Define x:(h) as the best linear predictor of x-h given Xt, Xt-1, ... Xt-h+1• Use the results from Question 1 to briefly comment on T(h). You do not need to provide any equations.

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