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)= σ². B)Var(u_t|y_{t - 1})= Var(y_t|y_t-1) σ². 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)= σ². B)Var(u_t|y_{t - 1})= Var(y_t|y_t-1)> σ². C)Var(u_t|y_{t - 1})< Var(y_t|y_t-1)= σ². D)Var(u_t|y_{t - 1})= Var(y_t|y_t-1)= σ².

Quizplus · Accepted Answer

For an AR(1) process to be homoskedastic, the variance of the error term at time 't' conditional on the dependent variable at time 't - 1' should be constant and independent of the value of the dependent variable at time 't - 1', i.e., Var(u_t|y_t-1) = σ^2. Additionally, the variance of the dependent variable at time 't' conditional on the dependent variable at time 't - 1' should also be constant and independent of the value of the dependent variable at time 't - 1', i.e., Var(y_t|y_t-1) = σ^2/(1 - ϕ^2). Therefore, the correct choice is D because it satisfies both conditions.

If Ut Refers to the Error Term at Time 'T

If U_t Refers to the Error Term at Time 'T