Time Series Modeler

The Time Series Modeler procedure estimates exponential smoothing, univariate Autoregressive Integrated Moving Average (ARIMA), and multivariate ARIMA (or transfer function models) models for time series, and produces forecasts. The procedure includes an Expert Modeler that attempts to automatically identify and estimate the best-fitting ARIMA or exponential smoothing model for one or more dependent variable series, thus eliminating the need to identify an appropriate model through trial and error. Alternatively, you can specify a custom ARIMA or exponential smoothing model.

Example. You are a product manager responsible for forecasting next month's unit sales and revenue for each of 100 separate products, and have little or no experience in modeling time series. Your historical unit sales data for all 100 products is stored in a single Excel spreadsheet. After opening your spreadsheet in IBM® SPSS® Statistics, you use the Expert Modeler and request forecasts one month into the future. The Expert Modeler finds the best model of unit sales for each of your products, and uses those models to produce the forecasts. Since the Expert Modeler can handle multiple input series, you only have to run the procedure once to obtain forecasts for all of your products. Choosing to save the forecasts to the active dataset, you can easily export the results back to Excel.

Statistics. Goodness-of-fit measures: stationary R-square, R-square (R ²), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), maximum absolute error (MaxAE), maximum absolute percentage error (MaxAPE), normalized Bayesian information criterion (BIC). Residuals: autocorrelation function, partial autocorrelation function, Ljung-Box Q. For ARIMA models: ARIMA orders for dependent variables, transfer function orders for independent variables, and outlier estimates. Also, smoothing parameter estimates for exponential smoothing models.

Plots. Summary plots across all models: histograms of stationary R-square, R-square (R ²), root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), maximum absolute error (MaxAE), maximum absolute percentage error (MaxAPE), normalized Bayesian information criterion (BIC); box plots of residual autocorrelations and partial autocorrelations. Results for individual models: forecast values, fit values, observed values, upper and lower confidence limits, residual autocorrelations and partial autocorrelations.

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Time Series Modeler Data Considerations

Data. The dependent variable and any independent variables should be numeric.

Assumptions. The dependent variable and any independent variables are treated as time series, meaning that each case represents a time point, with successive cases separated by a constant time interval.

Stationarity. For custom ARIMA models, the time series to be modeled should be stationary. The most effective way to transform a nonstationary series into a stationary one is through a difference transformation--available from the Create Time Series dialog box.
Forecasts. For producing forecasts using models with independent (predictor) variables, the active dataset should contain values of these variables for all cases in the forecast period. Additionally, independent variables should not contain any missing values in the estimation period.

Defining Dates

Although not required, it's recommended to use the Define Dates dialog box to specify the date associated with the first case and the time interval between successive cases. This is done prior to using the Time Series Modeler and results in a set of variables that label the date associated with each case. It also sets an assumed periodicity of the data--for example, a periodicity of 12 if the time interval between successive cases is one month. This periodicity is required if you're interested in creating seasonal models. If you're not interested in seasonal models and don't require date labels on your output, you can skip the Define Dates dialog box. The label associated with each case is then simply the case number.

To Use the Time Series Modeler

This feature requires the Forecasting option.

From the menus choose:
Analyze > Forecasting > Create Traditional Models...
On the Variables tab, select one or more dependent variables to be modeled.
From the Method drop-down box, select a modeling method. For automatic modeling, leave the default method of Expert Modeler. This will invoke the Expert Modeler to determine the best-fitting model for each of the dependent variables.
To produce forecasts:
Click the Options tab.
Specify the forecast period. This will produce a chart that includes forecasts and observed values.

Optionally, you can:

Select one or more independent variables. Independent variables are treated much like predictor variables in regression analysis but are optional. They can be included in ARIMA models but not exponential smoothing models. If you specify Expert Modeler as the modeling method and include independent variables, only ARIMA models will be considered.
Click Criteria to specify modeling details.
Save predictions, confidence intervals, and noise residuals.
Save the estimated models in XML format. Saved models can be applied to new or revised data to obtain updated forecasts without rebuilding models. This is accomplished with the Apply Time Series Models procedure.
Obtain summary statistics across all estimated models.
Specify transfer functions for independent variables in custom ARIMA models.
Enable automatic detection of outliers.
Model specific time points as outliers for custom ARIMA models.

Modeling Methods

The available modeling methods are:

Expert Modeler. The Expert Modeler automatically finds the best-fitting model for each dependent series. If independent (predictor) variables are specified, the Expert Modeler selects, for inclusion in ARIMA models, those that have a statistically significant relationship with the dependent series. Model variables are transformed where appropriate using differencing and/or a square root or natural log transformation. By default, the Expert Modeler considers both exponential smoothing and ARIMA models. You can, however, limit the Expert Modeler to only search for ARIMA models or to only search for exponential smoothing models. You can also specify automatic detection of outliers.

Exponential Smoothing. Use this option to specify a custom exponential smoothing model. You can choose from a variety of exponential smoothing models that differ in their treatment of trend and seasonality.

ARIMA. Use this option to specify a custom ARIMA model. This involves explicitly specifying autoregressive and moving average orders, as well as the degree of differencing. You can include independent (predictor) variables and define transfer functions for any or all of them. You can also specify automatic detection of outliers or specify an explicit set of outliers.

Estimation and Forecast Periods

Estimation Period. The estimation period defines the set of cases used to determine the model. By default, the estimation period includes all cases in the active dataset. To set the estimation period, select Based on time or case range in the Select Cases dialog box. Depending on available data, the estimation period used by the procedure may vary by dependent variable and thus differ from the displayed value. For a given dependent variable, the true estimation period is the period left after eliminating any contiguous missing values of the variable occurring at the beginning or end of the specified estimation period.

Forecast Period. The forecast period begins at the first case after the estimation period, and by default goes through to the last case in the active dataset. You can set the end of the forecast period from the Options tab.

This procedure pastes TSMODEL command syntax.