Questions / Quant research, Time-series reasoning
A centered smoother has an availability delay
A five-point centered moving average is M_t=(X_(t−2)+X_(t−1)+X_t+X_(t+1)+X_(t+2))/5. Each X_s becomes available at the end of period s. How many periods after the end of t can the final M_t first be computed?
Answer it in the app It's free. You get hints, a second try if you miss, and a follow-up question.
Show the answer and worked solution
Answer: 2 periods
- The last required observation is X_(t+2), available at the end of t+2. Therefore the final centered estimate for date t has a two-period delay, even though its plotted timestamp is t.
Interview shortcut. A centered window needs data k periods ahead: here 2.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.