Which smoothing constant makes an exponential smoothing forecast equivalent to a naïve forecast?

Using a smoothing constant of 1.0 in an exponential smoothing forecast yields results that are equivalent to a naïve forecast. In the context of forecasting, a naïve forecast simply uses the most recent observation as the next forecast, meaning that if the smoothing constant is set to 1.0, all weight in the forecast is placed entirely on the most recent data point.

Exponential smoothing works by taking a weighted average of past observations, and the smoothing constant determines how much weight is given to the most recent observation compared to the previous forecast. If the constant is set to 1.0, it indicates that the forecast will rely solely on the latest observation without any influence from historical data. Hence, this leads to a forecast that does not account for any historical trends or variations, which is precisely what the naïve method does.

In contrast, lower values for the smoothing constant (like 0.5, 0.8, or 0.9) would mean that past observations have some influence on the forecast, which differentiates those forecasts from the naïve approach. Therefore, when the smoothing constant is 1.0, the forecast is equal to the most recent data point, aligning it with the naïve forecasting method.