Holt Linear and Damped Trend Forecast Calculator
Calculate additive level/trend updates and ordinary or damped Holt point forecasts with explicit initialization and entered smoothing parameters.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Seed level with the first value and trend with the first difference, then apply the stated additive damped-level/trend recurrences.
ℓt=αyt+(1−α)(ℓprev+φbprev); bt=β(ℓt−ℓprev)+(1−β)φbprev
Worked example
For 10,12,14,16,18 with φ=1 and first-difference trend initialization, the model preserves level 18 and trend 2. The next three point forecasts are 20,22,24.
Assumptions and input details
2–1000 equally spaced observations; the table shows the last 100 and all requested future periods. Parameters are entered, not fitted or optimized. Initialization reuses the first two observations and is distinct from state-space estimated initialization. Forecast=final level+final trend×Σφ^j. No seasonality, uncertainty interval, backtesting, structural-break handling or accuracy guarantee is supplied. Negative projections remain visible.
References: Hyndman and Athanasopoulos: Holt and damped trend methods
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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