Practice — Time Series Fundamentals (5 questions)

Weekly signups are y = 20, 24, 22, 28. You fit simple exponential smoothing with \alpha = 0.5 and initial level \ell_1 = y_1 = 20.

1. Compute \ell_2, \ell_3, \ell_4 and the forecast for week 5.
2. Compute the in-sample one-step MAE and compare it with the naive forecast's MAE. Which does better, and by how much?
3. What happens to the forecast for week 20 if no new data arrives between week 5 and week 20? Why is this a limitation for a series with trend?