Which of the following is true of the exponential smoothing coefficient $\alpha$ in time series forecasting?

• A. It must satisfy $\alpha >1$
• B. It can be any positive real number
• C. It must always be equal to $1$
• D. It must satisfy $0<\alpha <1$

Answer: (D)

Verified step by step guidance

1. Understand that the exponential smoothing coefficient \( \alpha \) is a parameter used in time series forecasting to control the weighting of the most recent observation relative to past smoothed values.
2. Recall the definition of \( \alpha \): it is a smoothing constant that determines how quickly the weights decrease for older observations.
3. Recognize that \( \alpha \) must be a value between 0 and 1 (exclusive), meaning \( 0 < \alpha < 1 \), to ensure the weighted average properly balances recent and past data without overemphasizing or ignoring any part.
4. Note that if \( \alpha \) were greater than 1 or equal to 1, the model would place all weight on the most recent observation, losing the smoothing effect.
5. Similarly, if \( \alpha \) were less than or equal to 0, the model would not update based on new data, which defeats the purpose of exponential smoothing.