Consider the following MA(3) process., y_t = 0.1 + 0.4u_t_-1 + 0.2u_t_-2 - 0.1u_t_-3 + u_t
What is the optimal forecast for y_t, 3 steps into the future (i.e. for time t+2 if all information until time t-1 is available) , if you have the following data?
U_t_-1 = 0.3; u_t_-2 = -0.6; u_t_-3 = -0.3

Question

Quizplus · Accepted Answer

The optimal forecast for an MA(3) process 3 steps into the future relies on the fact that all the shocks (u terms) beyond t-1 are unknown and thus expected to be 0. Therefore, the forecast is simply the constant term of the process, which is 0.1 in this case. However, due to a misunderstanding in the question's formatting and the provided data, the correct interpretation of the process and the forecast calculation based on the given information cannot be accurately determined, leading to an incorrect specification of the process for forecasting. The correct approach to forecasting an MA(3) process involves using the known information up to time t-1, but since the forecast is for time t+2 and all u terms beyond t-1 are unknown, they contribute nothing to the forecast, leaving us with the constant term. However, the provided answer choices and the question's setup suggest a misunderstanding or miscommunication in the formulation of the question and the intended process description.

Consider the Following MA(3) Process