Overview (TSMODEL command)

The TSMODEL procedure estimates exponential smoothing, univariate Autoregressive Integrated Moving Average (ARIMA), and multivariate ARIMA (or transfer function models) models for time series, and the procedure produces forecasts. The procedure includes an Expert Modeler that attempts to identify and estimate an appropriate ARIMA or exponential smoothing model for each dependent-variable series. Alternatively, you can specify a custom ARIMA or exponential smoothing model.

Options

Automatic Model Identification. The Expert Modeler can identify an appropriate seasonal or nonseasonal ARIMA or exponential smoothing model for each dependent-variable series. If predictor variables are specified, the Expert Modeler selects, for inclusion in ARIMA models, those variables that have a statistically significant relationship with the dependent series. Model variables are transformed where appropriate by using differencing and/or a square root or natural log transformation. You can limit the set of candidate models to ARIMA models only or exponential smoothing models only.

Custom Models. You can specify a custom exponential smoothing or ARIMA model for one or more series. Seven exponential smoothing methods are available: simple, simple seasonal, Holt’s linear trend, Brown’s linear trend, damped trend, Winters’ additive, and Winters’ multiplicative. For ARIMA models, you can specify seasonal and nonseasonal autoregressive and moving average orders, differencing, as well as transfer functions for predictor variables. For exponential smoothing and ARIMA models, you can request that model variables be transformed prior to model estimation.

Outliers. If you use the Expert Modeler or specify a custom ARIMA model, TSMODEL can detect and model outlier time points automatically. The following outlier types can be identified: additive, additive patch, innovational, level shift, transient, seasonal additive, and local trend. Alternatively, if you request a custom ARIMA model, you can specify that one or more time points be modeled as outliers.

Output. Available output includes plots and tables that summarize the distribution of model goodness of fit, residual autocorrelations, and residual partial autocorrelations across models. In addition, you can obtain a table of model goodness of fit, Ljung-Box Q, and number of outliers by model. You can also obtain details for each model, including parameter estimates, forecasts, as well as autocorrelation and partial autocorrelation functions. Output can be restricted to the best-fitting or worst-fitting models based on goodness-of fit-values.

Saved Variables. You can save fit and forecast values to the active dataset as well as confidence intervals and noise residuals.

Missing Values. You can control whether user-missing values are treated as valid or invalid values.

Basic Specification

  • The basic specification is a MODEL subcommand that specifies one or more dependent-variable series.
  • By default, TSMODEL uses the Expert Modeler to identify and estimate the best ARIMA or exponential smoothing model for each series.
  • Default output includes a summary of the distribution of goodness of fit across estimated models and a table of stationary R-square, Ljung-Box Q, and number of outliers by model.

Syntax Rules

  • The following subcommands are global and apply to all models specified in a single instance of the TSMODEL command: MODELSUMMARY, MODELSTATISTICS, MODELDETAILS, SERIESPLOT, OUTPUTFILTER, SAVE, AUXILIARY, and MISSING.
  • Each global subcommand is optional, may be used only once, and must appear before any MODEL subcommand.
  • Models are specified in blocks. The MODEL subcommand indicates the start of a block. The MODEL subcommand must be used at least once.
  • The following subcommands apply to the preceding MODEL subcommand and constitute--along with a MODEL subcommand--a MODEL block: EXPERTMODELER, EXSMOOTH, ARIMA, TRANSFERFUNCTION, AUTOOUTLIER, and OUTLIER. An error occurs if any of these subcommands precedes the first MODEL subcommand.
  • The EXPERTMODELER, EXSMOOTH, and ARIMA subcommands are used within a MODEL block to specify the estimation method. If none of these subcommands is specified, the implicit default is EXPERTMODELER. An error occurs if more than one of these subcommands is specified within a MODEL block.
  • AUTOOUTLIER may be used only once within a MODEL block.
  • TRANSFERFUNCTION and OUTLIER may be used more than once within a MODEL block.
  • Each keyword may be specified only once within a subcommand.
  • Empty subcommands are not allowed; all subcommands must be specified with options.
  • All subcommands other than MODEL are optional.
  • Subcommand names and keywords must be spelled in full.
  • Subcommands can be specified in any order, with the exception that global subcommands must precede the first MODEL subcommand.
  • Equals signs (=) that are shown in the syntax chart are required.

Operations

  • TSMODEL honors time intervals and periodicity specified with the DATE command.
  • The procedure verifies that date variables that are implied by the current date specification exist and that their values coincide with the date specification within the estimation period. If SPLIT FILE is in effect, the check is done for each split. A split is skipped and a warning is issued if verification fails for that split. If the verification fails when SPLIT FILE is not in effect, an error occurs and processing terminates. If the data are filtered, values of date variables are verified within the filtered subset of data.
  • The procedure honors the estimation (historical) period that is defined with the USE command. However, depending on available data, the actual use period may vary by dependent variable. For a given dependent variable, the estimation period is the period left after eliminating contiguous missing values of the dependent variable at the beginning and end of the USE period.
  • If SPLIT FILE is in effect, and a split has fewer cases than implied by the USE period, a warning is issued and all available cases are used. If there are no cases in the USE period, the split is skipped altogether with a warning.
  • The PREDICT command defines the end of the forecast period for tables, charts, and model variables that are produced by TSMODEL. The forecast period always starts after the end of the estimation (USE) period. Like the estimation period, the forecast period can vary by model, depending on available data. If a PREDICT specification ends on or before the effective end of the USE period, the forecast period is empty.
  • The procedure does not honor the following commands: MODEL NAME or SAVE MODEL. Options for naming and saving models are provided with the TSMODEL procedure.
  • The procedure does not honor TSET. The TSMODEL procedure provides options for handling missing values, setting the width of confidence intervals, setting the maximum number of lags displayed for autocorrelations, and setting season length.
  • The TDISPLAY command does not display models that are saved by using TSMODEL.

Limitations

  • WEIGHT is ignored with a warning.