SPSS command: SPSS EXSMOOTH
Exponential smoothing with a parameter grid search
Exponential smoothing forecasts a series from weighted averages of its past, with separate weights for level, trend and season.
Free · No account · Files stay on your device · Updated 18 October 2026
What it tells you
Crosstabs runs the SPSS EXSMOOTH procedure: pick a trend (none, linear, exponential, damped) and a season (none, additive, multiplicative), and it tries every combination on the SPSS default grid to find the weights with the smallest sum of squared errors.
- Which smoothing weights (alpha, gamma, delta, phi) give the smallest sum of squared one-step errors.
- How sensitive the fit is to the weights, from the ten Smallest Sums of Squared Errors on the grid.
- The initial level and trend the recursions start from.
- How accurate the one-step forecasts were: mean error, MAE, MAPE, SSE, RMSE and Durbin-Watson.
- Forecasts for the next periods, with prediction intervals for the additive and linear-trend models.
When to use it
Use it when
- You want a transparent forecast whose behaviour you can explain: recent periods weigh more, older ones less.
- You know the shape of the series (e.g. linear trend plus a stable monthly pattern) and want to reproduce an EXSMOOTH specification.
- You want to fix the weights yourself to compare with an earlier SPSS run: untick the grid search and type them in.
Use something else when
- You are unsure which trend and season to choose: let TSMODEL's Expert Modeler compare models by normalized BIC.
- The series has gaps: EXSMOOTH needs a complete series, so fill missing time points by interpolation in step 1 or use ARIMA.
- Autocorrelation remains after smoothing or you need coefficient tests: an ARIMA model is the better tool.
How to run it in Crosstabs
- 01
Open Exponential smoothing
In Statistics mode, choose Exponential smoothing (EXSMOOTH) in the Forecasting group.
- 02
Define the time axis
Group rows into periods by a date or wave column, or use each row as a time point. Seasonal models need a Periodicity of 2 or more and at least two full cycles.
- 03
Choose the Series, Trend and Seasonality
Pick the Series, then set Trend to None, Linear, Exponential or Damped and Seasonality to None, Additive or Multiplicative: twelve models in all.
- 04
Search or fix the weights
Leave Grid search for the parameters (SPSS default grids) ticked, or untick it and type Alpha (level), Gamma (trend), Delta (season) and Phi (damping).
- 05
Set Periods to forecast and run
Enter the number of future periods (default 6) and click Run. The chart overlays observed values, the one-step fit and the forecast.
Worked example
Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.
Data
48 synthetic monthly values (January 2022 to December 2025) of a brand-tracker metric in percent: a level of 40 rising 0.25 points a month, a fixed seasonal pattern that peaks in December and dips in July, and normal noise (SD 1.1) from a fixed seed, so every build produces the same series.
| Parameter | Value |
|---|---|
| Alpha (level) | 0.10 |
| Gamma (trend) | 0.00 |
| Delta (season) | 0.00 |
| Initial level (S0) | 40.324 |
| Initial trend (T0) | 0.246 |
| Sum of squared errors | 56.767 |
Trend: Linear, Seasonality: Additive. Grid search over 396 combinations (SPSS default grids).
| Statistic | Value |
|---|---|
| Mean Error | −0.095 |
| Mean Absolute Error | 0.821 |
| Mean Absolute Percent Error | 1.806 |
| Root Mean Square Error | 1.087 |
| Durbin-Watson | 2.121 |
| Time point | Forecast | LCL (95%) | UCL (95%) |
|---|---|---|---|
| 2026-01 | 52.91 | 50.70 | 55.11 |
| 2026-02 | 52.92 | 50.71 | 55.13 |
| 2026-03 | 53.06 | 50.84 | 55.28 |
| 2026-04 | 52.72 | 50.48 | 54.95 |
| 2026-05 | 50.53 | 48.29 | 52.78 |
| 2026-06 | 50.64 | 48.39 | 52.90 |
How to read it
Holt-Winters additive smoothing (linear trend, additive season) is fitted by trying all 396 weight combinations; the smallest sum of squared one-step errors, 56.77, comes from alpha = 0.1, gamma = 0.0 and delta = 0.0. Weights of 0 for trend and season mean both stay at their initial estimates, which suits a series with a steady slope and a stable seasonal pattern. The one-step forecasts miss by 0.82 points on average (MAPE 1.81%), and the forecast for 2026-01 is 52.91.
Output tables explained
- Model Parameters
- The chosen weights, the initial level S0 and trend T0, and the sum of squared errors. The footnote gives the grid size or says the weights were fixed.
- Smallest Sums of Squared Errors
- The ten best weight combinations from the grid. If several rows have nearly the same SSE, the weights are poorly determined.
- Error Statistics
- Mean error, MAE, MAPE, SSE, RMSE and Durbin-Watson of the one-step-ahead fit. A Durbin-Watson far from 2 signals autocorrelated errors.
- Forecast
- Forecasts per future period. Intervals are an addition SPSS EXSMOOTH does not print, derived from the model's error-correction form; none are given for exponential trends or multiplicative seasons.
Assumptions and notes
- The series has no missing values within its observed span.
- Exponential trends and multiplicative seasons need every value to be positive.
- Initial seasonal factors come from a SEASON decomposition of the series, so seasonal models need at least two full cycles.
- The grid finds the best point on the grid, not a continuous optimum; TSMODEL optimises the weights continuously instead.
How the results are validated
For all twelve trend × season combinations, the initial level and trend (to 10 decimals), the fitted values at fixed weights (to 1e-10) and the grid-search best SSE and alpha are checked against an independent Python implementation of the SPSS manual's recursions. For the additive and non-seasonal trend models, those recursions are in turn matched to statsmodels ExponentialSmoothing with the same initial states to 1e-10. Validation evidence
Questions
What do alpha, gamma, delta and phi do?
Alpha updates the level, gamma the trend, delta the seasonal factors and phi damps the trend. Values near 1 react quickly to recent data; values near 0 keep that component almost fixed.
Which grid does the search use?
The SPSS defaults: alpha 0 to 1 by 0.1, gamma and delta 0 to 1 by 0.2, and phi 0.1 to 0.9 by 0.2. Only the weights the chosen model uses are searched.
Additive or multiplicative seasonality?
Use additive when the seasonal swing stays about the same size as the level changes, multiplicative when it grows in proportion to the level. Multiplicative needs positive values.
Why do my forecasts have no intervals?
SPSS EXSMOOTH prints none. Crosstabs adds intervals where the model has an additive error-correction form; for exponential trends or multiplicative seasons it shows point forecasts only.
How is this different from TSMODEL's smoothing?
EXSMOOTH searches a fixed grid and starts from SEASON-based initial values, as the SPSS EXSMOOTH command does. TSMODEL optimises the weights continuously, back-casts the initial states and reports standard errors and normalized BIC.
Related procedures
- Time Series Forecasting (Expert Modeler)TSMODEL
- Seasonal DecompositionSEASON
- ARIMAARIMA
- Forecast Goodness of FitFIT
- Create Time SeriesCREATE
- Free SPSS alternative: full coverage list
Run Exponential Smoothing on your own data
Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.
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