How to use the exponential smoothing forecast calculator
- Paste your values in time order, separated by commas, spaces or new lines. You need at least 3.
- Enter the smoothing weight, alpha, between 0 and 1. The 0.3 shown is an example.
- Read the forecast for the next period, the errors of the one-step forecasts and the alpha with the smallest error.
- Check the table to see each actual value, the forecast made before it, the new level and the error.
Formula
level 1 = first value
level t = alpha x value t + (1 - alpha) x level t-1
forecast for period t = level t-1
error t = value t - forecast t
forecast for the next period = the last level
A higher alpha follows recent values more closely, and a lower alpha smooths more. The page also tries alpha from 0.05 to 0.95 in steps of 0.05 and shows the one with the smallest squared error.
Ten monthly values
For the values 112, 118, 132, 129, 121, 135, 148, 148, 136 and 119 with alpha 0.3, the second level is 0.3 x 118 + 0.7 x 112 = 113.8, and the last level, the forecast for the next period, is 131.445. The nine one-step errors have a mean absolute error of 11.662 and a root mean squared error of 13.703.
The alpha with the smallest squared error in steps of 0.05 is 0.95, whose forecast is 119.880. A high alpha wins here because the values move up and down quickly, and a forecast near the latest value does better than a heavily smoothed one.
What the method assumes
Simple exponential smoothing has no trend and no season. It forecasts a flat line at the latest level. It suits data that wander around a steady level, such as stable daily demand. If your data climb or repeat each year, use a method with a trend or a seasonal part, or compare the result with a plain average.
Picking alpha
Choosing the alpha with the lowest past error is easy but can overfit a short series, since it fits the past rather than the future. A mid-range value such as 0.2 to 0.4 is a common starting point. Compare the errors for a few values of alpha and prefer one that does well across the series rather than on a lucky stretch.
Related data tools
Compare with a Moving Average Calculator, summarize the spread with the Descriptive Statistics Calculator or the Standard Deviation Calculator, and plan sales with the Sales Forecast Calculator.
Assumptions and limits
- Values are equally spaced in time and listed from oldest to newest.
- The first level is the first value, and errors start at the second value.
- Alpha is the same for the whole series.
- A forecast is not a promise, and the page gives no range of likely values.
Frequently asked questions
How do you calculate exponential smoothing?
Start with the first value as the level. Then each new level is alpha times the new value plus one minus alpha times the old level. The last level is the forecast.
What value of alpha should I use?
There is no single best value. The page starts with 0.3 and shows the alpha with the smallest past error so you can compare. Short series can mislead, so prefer a value that does well across the series.
Why is my forecast a flat line?
Simple exponential smoothing has no trend or season, so every future period gets the same forecast, the last level.
How many values do I need?
At least 3 for the page to work, but more is better. With very few values the errors and the best alpha are not reliable.