Question

Let Y_t = 1 + 12Y_t1 2Y_t2 + e_t be an autoregressive process of order 2, where e_t is a white noise with mean zero and variance 2.

Determine the YuleWalker equation of the process.
YuleWalker equation
(A) R_1 = 12R_0 2R_1
(B) R_2 = 12R_1 2R_0
(C) R_2 = 12R_0 2R_1
(D) R_1 = 12R_0 + 2R_1

Answer 1

The correct Yule-Walker equation for the given AR(2) process Y_t = 1 + 12Y_t-1 - 2Y_t-2 + e_t is R_2 = 12R_1 - 2R_0.

Step-by-step explanation:

The student is asking about the Yule-Walker equations for an autoregressive process of order 2 (AR(2)). The equation for the process is given, and we need to find the correct Yule-Walker equation that represents the process. Given the AR(2) process, Yt = 1 + 12Yt-1 - 2Yt-2 + et, where et is white noise with zero mean and variance of 2, we can derive the Yule-Walker equations by correlating both sides of the AR process with Yt-1 and Yt-2 to find expressions for R1 and R2 respectively.

For lag-1, we have R1 = 12R0 - 2R1, and for lag-2, we have R2 = 12R1 - 2R0. Hence, the correct Yule-Walker equation option is (B) R2 = 12R1 - 2R0.