One-Step-Ahead Prediction of the Disturbance

The viewer can (1) split v(t) into the new kick e(t) and the known part m(t−1), (2) explain why the best guess sets e(t) to its mean, zero, (3) derive v̂(t|t−1) = (1 − H⁻¹)v(t) one step at a time, and why it only uses past v, (4) apply it to AR(1) (v̂ = a v(t−1)) and MA(1).