SPSS command: SPSS TSMODEL

Time series forecasting with an Expert Modeler

TSMODEL fits a forecasting model to one series and projects it forward with prediction intervals.

Run Time Series Forecasting (Expert Modeler) in your browser All SPSS procedures

Free · No account · Files stay on your device · Updated 18 October 2026

What it tells you

In Crosstabs you can let an Expert Modeler compare exponential smoothing and ARIMA candidates by normalized BIC, or name one of seven smoothing models yourself; the model statistics follow the SPSS TSMODEL definitions.

Which model type describes the series best among the candidates tried, ranked by normalized BIC in the Candidate Models table.
How well the chosen model fits: stationary R², R², RMSE, MAPE, MaxAPE, MAE, MaxAE and normalized BIC.
Whether structure is left in the residuals, from the Ljung-Box Q(18) test.
The smoothing weights or ARIMA coefficients with standard errors and significance.
Point forecasts for the next periods with 95% lower and upper confidence limits.

When to use it

Use it when

You track a metric over waves or months (awareness, NPS, share of purchase intent) and need a defensible forecast for the next quarter or year.
You do not know whether a trend or seasonal model suits the data and want candidates compared on one criterion.
Your file has one row per respondent with an interview date: the time-axis step aggregates rows into period means, sums or percentages before modelling.

Use something else when

You need predictors, interventions or transfer functions: TSMODEL here is univariate, and the Expert Modeler does not detect outliers (ARIMA with a chosen order can).
You already know the ARIMA orders you want: use the ARIMA procedure to set p, d, q and the seasonal orders directly.
You only need to describe the seasonal pattern, not forecast: seasonal decomposition gives the seasonal factors directly.
There are only a handful of periods; with fewer than six values the Expert Modeler will not run, and short series make any forecast fragile.

How to run it in Crosstabs

01
Open the data in Statistics mode
Open a .sav, CSV or Excel file in the workspace, switch to Statistics mode and choose Create forecasting models (TSMODEL) in the Forecasting group.
02
Define the time axis
Either group respondent rows into periods by a date or wave column (with Period length when dates are detected), or treat each row as one time point in file order. Set the Periodicity, e.g. Monthly (12) or Quarterly (4).
03
Choose the Dependent series
Pick the variable to forecast. With respondent rows, choose the Value per period: Mean, Sum, or Percent in a category.
04
Pick a Method
Choose Expert Modeler: all models, exponential smoothing only or ARIMA only, or one of the seven exponential smoothing models (Simple, Brown, Holt, Damped trend, Simple seasonal, Winters' additive, Winters' multiplicative).
05
Set Periods to forecast and run
Enter how many periods to forecast (0–120) and click Run. The candidate search runs in a background worker so the page stays responsive.

Run Time Series Forecasting (Expert Modeler) in your browser

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.

Model Description

Series	Model Type
awareness	Winters' additive

Chosen by the smallest normalized BIC among the candidates; Expert Modeler: exponential smoothing only, periodicity 12.

Model Fit

Fit Statistic	Value
Stationary R-squared	0.760
R-squared	0.941
RMSE	1.061
MAPE	1.860
MAE	0.847
Normalized BIC	0.360

Candidate Models

Model Type	Normalized BIC
Winters' additive	0.360
Winters' multiplicative	0.684
Simple seasonal	0.821
Simple	1.517
Holt	1.591
Damped trend	1.713

For a positive seasonal series the exponential smoothing expert compares six models.

Forecast

Time point	Forecast	LCL (95%)	UCL (95%)
2026-01	53.00	50.93	55.08
2026-02	52.48	50.38	54.57
2026-03	52.65	50.53	54.77
2026-04	52.74	50.60	54.89
2026-05	50.49	48.32	52.66
2026-06	50.06	47.86	52.26

How to read it

Out of 6 exponential smoothing candidates, the Expert Modeler picks Winters' additive with normalized BIC 0.360. It explains R² = 0.941 of the variation with a typical one-step error (RMSE) of 1.06 points, and the Ljung-Box Q(18) = 18.21 (p = .252) finds no remaining autocorrelation in the residuals. The forecast for 2026-01 is 53.00 with a 95% interval from 50.93 to 55.08.

Output tables explained

Model Description: The series and the chosen model type, with a note saying whether it won on normalized BIC or whether a short series limited the search to exponential smoothing.
Model Fit: Stationary R², R², RMSE, MAPE, MaxAPE, MAE, MaxAE and normalized BIC on the original scale. RMSE divides by n − k, the number of fitted points minus estimated parameters.
Model Statistics: Ljung-Box Q(18) on the residuals with its df and significance. A small p value means autocorrelation is left. Number of Outliers is always 0 because outlier detection is not available.
Exponential Smoothing Model Parameters: Alpha (level), Gamma (trend), Delta (season) and Phi (damping) as used by the model, with standard errors, t and significance; ARIMA winners show Parameter Estimates instead.
Forecast: One row per future period with the forecast and its LCL and UCL at 95%. Winters' multiplicative forecasts have no interval because the model has no equivalent ARIMA form.
Candidate Models: Every model the Expert Modeler estimated, smallest normalized BIC first (up to 25 rows), so you can see how close the runners-up were.

Assumptions and notes

Each period value is treated as one observation; the sampling error of each period's survey estimate is not included in the intervals.
The pattern seen so far continues: forecasts assume no structural break, outlier or external shock in the forecast window.
Seasonal models need the periodicity from step 1 and at least two full cycles; Winters' multiplicative needs positive values.
The series must end with an observed value so forecasts start from the latest period.

How the results are validated

The smoothing recursions for the Simple, Holt, damped, Winters' additive and Winters' multiplicative models are checked against statsmodels ExponentialSmoothing with the same initial states, agreeing to 1e-9; the ARIMA candidates use the ARIMA engine tested against statsmodels. Tests also confirm that the optimised Winters' additive weights sit at a local SSE minimum and that short series use exponential smoothing only. SPSS does not publish its ARIMA identification rules, so the Expert Modeler's ARIMA search (KPSS and seasonal-strength differencing, then a stepwise normalized-BIC search) is a documented substitute and can pick a different model than SPSS. Validation evidence

Questions

How does the Expert Modeler choose a model?

It fits a set of exponential smoothing models (four non-seasonal, or five or six seasonal ones) and a stepwise set of ARIMA models, then keeps the one with the smallest normalized BIC. Series shorter than max(20, 3 × periodicity) are limited to exponential smoothing, as SPSS specifies.

Will it pick the same model as SPSS?

Often for exponential smoothing, not guaranteed for ARIMA. SPSS's ARIMA identification rules are unpublished, so differencing is chosen here by seasonal strength and KPSS tests and orders by a stepwise BIC search; the Candidate Models footnote says so.

What does normalized BIC mean?

It is ln(MSE) + k·ln(n)/n: the log of the mean squared error plus a penalty for the number of parameters. Lower is better, and it is only comparable between models fitted to the same series.

Can I forecast from respondent-level survey data?

Yes. In step 1 choose the date or wave column and the panel builds one value per period (mean, sum or percent in a category), applying the case weight. The model then treats each period value as one observation.

Why are there no prediction intervals for Winters' multiplicative?

Intervals are derived from each model's equivalent ARIMA form, and the multiplicative Winters model has none, so only point forecasts are shown.

Run Time Series Forecasting (Expert Modeler) on your own data

Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.

Open the workspace

SPSS is a trademark of IBM Corp. Crosstabs is not affiliated with or endorsed by IBM.