Exponential Smoothing Calculator

Forecast Results

Detailed Calculation Table

Period	Actual	Level	Trend	Seasonal	Fitted	Forecast	Lower	Upper	Residual	Absolute Error	Squared Error	Percentage Error

Merged Results

Data and Model Settings

Observations

Use date,value rows or a single value per line.

Upload CSV

Date column

Value column

Smoothing method Seasonal period

Common values are 4, 7, 12, 24, and 52.

Detect seasonal period automatically

Forecast horizon

Smoothing parameters

Optimize parameters automatically

Alpha (level) Beta (trend) Gamma (seasonal) Phi (damping)

Initialization method Initial level Initial trend Initial seasonal indices

Confidence level Validation holdout

20% of recent data

Use rolling-origin validation score

Include fitted historical values

Include prediction intervals

Missing-value handling

Outlier handling

Transformation

Date aggregation

Model selection metric

Future period labels

Model Settings File

Import Settings JSON

Formula Used

Simple smoothing: L_t = αY_t + (1 − α)L_t−1.

Holt level: L_t = αY_t + (1 − α)(L_t−1 + T_t−1).

Holt trend: T_t = β(L_t − L_t−1) + (1 − β)T_t−1.

Additive seasonality: S_t = γ(Y_t − L_t) + (1 − γ)S_t−m.

Multiplicative seasonality: S_t = γ(Y_t / L_t) + (1 − γ)S_t−m.

How to Use

Enter time-series observations or upload a CSV file.
Select a smoothing method or automatic model selection.
Choose seasonal, validation, and preprocessing settings.
Enable optimization or enter manual parameter values.
Calculate, inspect charts, and export the results.

Example Data

Month	Observed demand	Expected purpose
January	120	Initial level
February	128	Trend detection
March	125	Short-term variation
April	137	Forecast adjustment

Frequently Asked Questions

What does alpha control?

Alpha controls how quickly the level responds. Larger values emphasize recent observations.

When should Holt smoothing be used?

Use Holt smoothing when the series has a trend. It does not model seasonality.

What is damped trend?

Damping gradually reduces a projected trend. It often prevents unrealistic long-range forecasts.

Additive or multiplicative seasonality?

Additive effects stay roughly constant. Multiplicative effects grow with the series level.

How much seasonal data is needed?

Use at least two complete seasonal cycles. More cycles usually improve parameter estimates.

What does automatic selection do?

It tests eligible models and parameter combinations. The selected metric determines the winner.

How are intervals calculated?

Intervals use residual variability and a normal approximation. They widen across future periods.

Can negative values be modeled?

Most methods accept negative observations. Multiplicative seasonality and logarithms require positive values.

Does this replace a forecasting library?

No. It supports exploration and transparent calculations. Production systems should use validated statistical software.