Questions / Quant research, Time-series reasoning

A centered smoother has an availability delay

Foundation, about 6 minutes. Question R173.

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?

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Answer: 2 periods

  1. 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.

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