Suppose we use an AR (2) model to predict the next value of a random process based on observations of the two most recent samples That is, we form n 1 a1Y n a2Y n 1 (a) Derive an expression for the mean square estimation error, E 2 E (Y n 1 (n 1 ) 2 (b) Find the values of the prediction coefficient...

a E 2 E Y n 1 a 1 Y n a 2 Y n 1 2 R YY 01 a 2 1 a 2 2 2a 1 1 a ...

Suppose we use an AR (2) model to predict the next value of a random process based

Question:

Suppose we use an AR (2) model to predict the next value of a random process based on observations of the two most recent samples. That is, we form
Ẏ [n + 1] = a1Y [n] + a2Y [n – 1]
(a) Derive an expression for the mean- square estimation error,
E [Ɛ2] = E [(Y n +1] –Ẏ [(n + 1]) 2]
(b) Find the values of the prediction coefficients, a1 and a2, that minimize the mean-square error.