KEVOS® MAKEOS · Planning
Holt Trend Forecast (Double Exponential Smoothing, Level and Trend, Forecast Error)
My demand or usage is rising (or falling) steadily: what does double exponential smoothing forecast for the next few periods, how large is its error on my history, and which smoothing constants would have done best?
Double exponential smoothing (Holt’s method) from up to twelve periods of demand or usage: the smoothed level and trend from your two smoothing constants and starting trend, the one-step forecast errors on the history, the mean squared error and RMSE as a share of average demand, the forecast for the period you choose ahead, and the pair of constants with the smallest error found by trial, against the error you accept.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of periods used | periods | How many periods below to use, oldest first (at least 4). |
| Level smoothing constant α | Weight on the latest actual value when updating the level (0 to 1). | |
| Trend smoothing constant γ | Weight on the latest change in level when updating the trend (0 to 1). | |
| Starting trend b₁ | choice | How to set the trend at the first period; NIST lists all three. |
| Periods ahead to forecast | periods | How many periods past the last actual value to forecast. |
| Forecast error accepted (RMSE) | % of average | Largest root mean squared forecast error you accept, as a share of average demand. |
| Demand in each period, oldest first | ||
| Period 1 demand | units | Actual demand or usage in period 1, oldest first. |
| Period 2 demand | units | Actual demand or usage in period 2, oldest first. |
| Period 3 demand | units | Actual demand or usage in period 3, oldest first. |
| Period 4 demand | units | Actual demand or usage in period 4, oldest first. |
| Period 5 demand | units | Actual demand or usage in period 5, oldest first. |
| Period 6 demand | units | Actual demand or usage in period 6, oldest first. |
| Period 7 demand | units | Actual demand or usage in period 7, oldest first. |
| Period 8 demand | units | Actual demand or usage in period 8, oldest first. |
| Period 9 demand | units | Actual demand or usage in period 9, oldest first. |
| Period 10 demand | units | Actual demand or usage in period 10, oldest first. |
| Period 11 demand | units | Actual demand or usage in period 11, oldest first. |
| Period 12 demand | units | Actual demand or usage in period 12, oldest first. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of periods used
- What it is
- How many of the demand periods listed below are used, counting from the oldest.
- Units and format
- Enter a number in periods: periods. The form accepts 4 periods to 12 periods. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 periods as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Periods beyond this count are ignored.
- Get it right
- Use at least eight periods to judge the error and choose the constants.
What this means: Level smoothing constant α
- What it is
- The level smoothing constant: the weight given to the latest actual demand when updating the smoothed level, between 0 and 1.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3623 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger constant follows recent demand more closely but also follows random noise.
- Get it right
- Start from the best value the tool finds on your history, then round it.
What this means: Trend smoothing constant γ
- What it is
- The trend smoothing constant: the weight given to the latest change in level when updating the trend, between 0 and 1.
- Units and format
- Enter a plain number with no unit. The form accepts 0.01 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger constant lets the trend swing with each period’s change.
- Get it right
- A smaller value keeps a steadier trend; check the best value on your history.
What this means: Starting trend b₁
- What it is
- How the starting trend is set from the first periods of history; NIST gives all three choices.
- Units and format
- Choose one of 3 options from the list: Average of the first three changes; First change (y₂ − y₁); Average change over all periods.
- Example
- The form opens with “Average of the first three changes” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the early forecasts most; its effect fades as γ and the number of periods grow.
- Get it right
- The average of the first three changes is a good default; the first change alone is sensitive to noise.
What this means: Periods ahead to forecast
- What it is
- How many periods past the last actual period to forecast; the tool lists every period up to it.
- Units and format
- Enter a number in periods: periods. The form accepts 1 periods to 24 periods. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 periods as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The forecast moves by one trend step for each extra period ahead.
- Get it right
- Keep it short: a straight trend projected far ahead becomes unreliable.
What this means: Forecast error accepted (RMSE)
- What it is
- The largest root mean squared forecast error you accept, as a share of average demand over the periods used.
- Units and format
- Enter a number in % of average: % of average. The form accepts 0.1 % of average to 100 % of average. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 % of average as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line.
- Get it right
- Set it from the safety stock or capacity buffer you are prepared to hold against forecast error.
Demand in each period, oldest first
What this means: Period 1 demand
- What it is
- Actual demand or usage in period 1, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6.4 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the starting trend as well as the level and errors after it.
- Get it right
- The first period starts the level (S₁ = y₁), so avoid starting on an unusual period.
What this means: Period 2 demand
- What it is
- Actual demand or usage in period 2, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5.6 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the starting trend as well as the level and errors after it.
- Get it right
- Use actual demand for period 2, not shipments cut short by stock-outs.
What this means: Period 3 demand
- What it is
- Actual demand or usage in period 3, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7.8 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the starting trend as well as the level and errors after it.
- Get it right
- Use actual demand for period 3, not shipments cut short by stock-outs.
What this means: Period 4 demand
- What it is
- Actual demand or usage in period 4, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8.8 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the starting trend as well as the level and errors after it.
- Get it right
- Use actual demand for period 4, not shipments cut short by stock-outs.
What this means: Period 5 demand
- What it is
- Actual demand or usage in period 5, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 5, not shipments cut short by stock-outs.
What this means: Period 6 demand
- What it is
- Actual demand or usage in period 6, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 11.6 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 6, not shipments cut short by stock-outs.
What this means: Period 7 demand
- What it is
- Actual demand or usage in period 7, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 16.7 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 7, not shipments cut short by stock-outs.
What this means: Period 8 demand
- What it is
- Actual demand or usage in period 8, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15.3 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 8, not shipments cut short by stock-outs.
What this means: Period 9 demand
- What it is
- Actual demand or usage in period 9, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21.6 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 9, not shipments cut short by stock-outs.
What this means: Period 10 demand
- What it is
- Actual demand or usage in period 10, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 22.4 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 10, not shipments cut short by stock-outs.
What this means: Period 11 demand
- What it is
- Actual demand or usage in period 11, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 24.9 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 11, not shipments cut short by stock-outs.
What this means: Period 12 demand
- What it is
- Actual demand or usage in period 12, counting from the oldest period entered.
- Units and format
- Enter a number in units: a count of units. The form accepts 0 units or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 27.3 units as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Changes the level, trend and forecast errors from this period on; recent periods weigh most.
- Get it right
- Use actual demand for period 12, not shipments cut short by stock-outs.
Method and formulas
- S₁ = y₁ and b₁ from the chosen start; Sₜ = α yₜ + (1 − α)(Sₜ₋₁ + bₜ₋₁); bₜ = γ (Sₜ − Sₜ₋₁) + (1 − γ) bₜ₋₁ (NIST e-Handbook 6.4.3.3).
- One-step forecast for period t is Sₜ₋₁ + bₜ₋₁; errors for t = 2 to n give MSE = Σ e² ÷ (n − 1); forecast m periods ahead = Sₙ + m bₙ (NIST 6.4.3.4).
- The best α and γ are found by trial over 0.01 to 1 in steps of 0.01.
- Example: level 22.815, trend 2.9568 per period; forecast 37.599 at the last period ahead; RMSE 1.9168 (15.07 % of average).
Limitations
- Projects a straight-line trend: it overshoots when growth levels off and does not model seasonal patterns (NIST 6.4.3.5 covers triple smoothing).
- The best constants on a short history are uncertain; forecasts several periods ahead grow less reliable.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Forecast demand for a part whose sales are growing
- Plan capacity or stock for a rising workload
- Compare trend smoothing with simple smoothing on the same history
Who it is for
- Production and inventory planners
- Operations managers
- Sales and purchasing staff
What you get
- Level and trend after the last period
- Mean squared error and RMSE
- Forecasts for the periods ahead
- Best pair of smoothing constants on this history
Interpreting the result
- A best γ near 1 means the trend follows the latest change in level; a small γ keeps a steadier trend. NIST notes that regression gives a more conservative projection than double smoothing.
References
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.4.3.3 Double Exponential Smoothing — https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc433.htm
- NIST/SEMATECH e-Handbook of Statistical Methods, 6.4.3.4 Forecasting with Double Exponential Smoothing (LASP) — https://www.itl.nist.gov/div898/handbook/pmc/section4/pmc434.htm
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Useful alongside · Library collection
Demand forecasting for small manufacturers: matching supply with demand without drowning in stock
In Manufacturing Operations and Design for Manufacture
What it covers: Practical forecasting and planning for small manufacturers: simple forecasting methods, measuring forecast error, safety stock, reorder points, order quantities and a monthly planning meeting.
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