In a cumulative mean time series forecast, the forecast equals which of the following?

• A. Average of all prior observations, unbiased
• B. Last observation
• C. Average of last M observations
• D. Weighted mean of prior data

Answer: (A)

A cumulative mean forecast uses the average of all observations observed so far to predict the next value. After t observations, the forecast for the next period is (x1 + x2 + ... + xt) / t, giving equal weight to every past data point. This running mean is a natural neutral predictor: as more data accumulate, it stabilizes toward the underlying mean of the process, and, under standard assumptions, its expected value equals the true mean (unbiased).

This differs from using the last observation, which only reflects the most recent point and ignores the history; from averaging only the most recent M observations, which is a moving average that discards older data; and from a weighted mean that assigns different weights to observations. The cumulative mean keeps a simple, equal-weighted average of all past data, which is why it represents the forecast in this approach.