Statistik & Wahrscheinlichkeit
Verifizierter Rechner mit transparenter Formel
Exponential Smoothing Calculator.
Calculates the smoothed value for the next period using simple exponential smoothing, given the most recent actual value, the previous smoothed value, and a smoothing constant alpha.
Ihre Eingaben
So funktioniert es
- 1
Enter the most recent actual observation.
- 2
Enter the previous smoothed value (or initial forecast).
- 3
Choose the smoothing constant alpha between 0 and 1.
- 4
The calculator computes the new smoothed value as alpha times actual plus (1 minus alpha) times previous smoothed.
alpha * actual + (1 - alpha) * previous_smoothedHäufig gestellte Fragen
What does alpha represent?
Alpha is the smoothing constant. Higher alpha gives more weight to the most recent actual value, making the forecast more responsive to changes. Lower alpha makes the forecast smoother and less reactive.
How do I choose alpha?
Common practice is to try values between 0.1 and 0.3 for stable series, and higher values (0.5-0.9) for series with sudden changes. You can also optimize alpha by minimizing forecast errors on historical data.
What if I don't have a previous smoothed value?
If no previous smoothed value exists, you can use the first actual observation as the initial smoothed value, or the average of the first few observations.
Diese Rechner-Kategorie erkunden
Ergebnisse
Formel geprüftNext smoothed value
113
Schätzung nur zur allgemeinen Orientierung – wichtige Entscheidungen mit einem geeigneten Fachmann verifizieren.
So funktioniert es
Calculates the smoothed value for the next period using simple exponential smoothing, given the most recent actual value, the previous smoothed value, and a smoothing constant alpha.
- Enter the most recent actual observation.
- Enter the previous smoothed value (or initial forecast).
- Choose the smoothing constant alpha between 0 and 1.
- The calculator computes the new smoothed value as alpha times actual plus (1 minus alpha) times previous smoothed.
Formeln
Die Mathematik hinter diesem Rechner, aufgeschrieben, damit Sie das Ergebnis überprüfen können.
Simple Exponential Smoothing
The new smoothed value S_t is a weighted average of the current actual value X_t and the previous smoothed value S_{t-1}.
Example:
Input: X_t = 120, S_{t-1} = 110, α = 0.3
Calculation: 0.3*120 + 0.7*110 = 36 + 77 = 113
Result: S_t = 113
Anwendungsfälle im Alltag
Wo diese Berechnung im täglichen Leben vorkommt.
Demand Forecasting
Smooth sales or demand data to generate short-term forecasts for inventory management.
Example: Forecast next month's sales based on this month's actual and previous forecast.
Trend Analysis
Remove random fluctuations from time series data to identify underlying trends.
Example: Smooth weekly website traffic to see the overall direction.
Quality Control
Monitor process measurements to detect shifts while filtering out noise.
Example: Track the smoothed average of product weights to ensure consistency.
Tipps und häufige Fehler
Tips
- Start with alpha = 0.2 and adjust based on how quickly you want the forecast to react.
- Use a holdout sample to test different alpha values and pick the one with lowest error.
- For very noisy data, use a smaller alpha to avoid overreacting to random fluctuations.
- If the series has a trend, consider double exponential smoothing instead.
Common Mistakes to Avoid
- Using alpha > 1 or < 0; alpha must be between 0 and 1.
- Forgetting to update the smoothed value each period; always use the latest smoothed value as the previous one.
- Assuming exponential smoothing works well for data with strong seasonality without adjustments.
Annahmen und Einschränkungen
- Use the stated inputs and units.
- Results are estimates for planning and education.
- Check measurements and source data before making an important decision.