If u_t refers to the error term at time 't' and y_{t -} ₁ refers to the dependent variable at time 't - 1', for an AR(1) process to be homoskedastic, it is required that: A)Var(u_t|y_{t -} ₁) Var(y_t|y_t-₁) = ². B)Var(u_t|y_{t -} ₁) = Var(y_t|y_t-₁) ². C)Var(u_t|y_{t -} ₁)

Question

If u_t refers to the error term at time 't' and y_{t -} ₁ refers to the dependent variable at time 't - 1', for an AR(1) process to be homoskedastic, it is required that: A)Var(u_t|y_{t -} ₁) > Var(y_t|y_t-₁) = ². B)Var(u_t|y_{t -} ₁) = Var(y_t|y_t-₁) > ². C)Var(u_t|y_{t -} ₁) < Var(y_t|y_t-₁) = ². D)Var(u_t|y_{t -} ₁) = Var(y_t|y_t-₁) = ².

Quizplus · Accepted Answer

For an AR(1) process to be homoskedastic, it is required that the conditional variance of the error term is constant across time. Therefore, Var(u_t|y_{t -} ₁) should be equal to Var(u_t|₁), and Var(y_t|y_t-₁) should be equal to Var(y_t|₁). Hence, the correct choice is D, which states that both variances are equal. The other choices suggest that one variance is greater than the other, which would mean the process is heteroskedastic.

If Ut Refers to the Error Term at Time 'T

If U_t Refers to the Error Term at Time 'T