quiz_3 - AMS316 Quiz#3 1 Compute the ACF(k(k 0 of the AR(2...

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AMS316 Quiz #3 1. Compute the ACF ρ ( k ) ( k 0) of the AR(2) process 8 X t = 2 X t - 1 + X t - 2 + Z t , in which Z t are i.i.d. standard normal random variables. 2. Consider the stationary AR(2) process x t = α 1 x t - 1 + α 2 x t - 2 + z t , in which z t are i.i.d. normal random variables with mean 0 and variance σ 2 . The observations we have are x 1 , . . . , x n . (a) What is the 1-step ahead forecast at the forcast origin x n , i.e., x n (1)? What is the forcast error and its variance? (b) What is the 2-step ahead forecast at the forcast origin x n , i.e., x n (2)? What is the forcast error and its variance? (c) What is the k -step ahead forecast at the forcast origin x n , i.e., x n ( k ), for k 3? (It is OK to write down the recursive formula for x n ( k )) 3. Consider the stationary and invertible ARMA(1,1) process x t - αx t - 1 = z t - θz t - 1 , in which z t are i.i.d. normal random variables with mean 0 and variance σ 2 . The observations we have are x 1 , . . . , x n . (a) What is the 1-step ahead forecast at the forcast origin
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This note was uploaded on 08/08/2010 for the course AMS 316 taught by Professor Xing during the Fall '09 term at SUNY Stony Brook.

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