Modeling Specifications
The Modeling Specifications section in the Time Series Forecast report enables you to fit models to the individual time series. A variety of models are considered. Hyndman et al. (2008) defines state space smoothing models based on their error, trend component, and seasonal component:
• The errors can be additive (A) or multiplicative (M).
• The trend component can be none (N), additive (A), additive damped (Ad), multiplicative (M), or multiplicative damped (Md).
• The seasonal component can be none (N), additive (A), or multiplicative (M).
A specific model can be represented by its ETS (Error, Trend, Seasonal). These are the models used in Time Series Forecasting.
There are two tabs in the Modeling Specifications report. Use the Recommended Specifications tab to fit a set of state space smoothing models that is chosen by the platform. Use the Complete Specifications tab to select the specific state space smoothing models that you want to fit. For each individual time series, the best fitting model from the given set is then used for forecasting.
Select Models
Available only in the Complete Specifications tab, shown in Complete Specifications Tab. The Select Models report enables you to specify the state space smoothing models to fit to the individual time series. Use the check boxes to select the error, trend, and seasonality for the models. Click Select Recommended to select the check boxes that correspond to the models recommended by the platform. Click Select All to select all check boxes or Deselect All to deselect all check boxes. The Constrain Parameters option is selected by default, which constrains the parameters in such a way that the further an observation is from the present, the less effect it has on the present state of the model. In State Space Smoothing models, a forecast at time t, given all previous observations, is the same as the weighted sum of all observations up to time t. The weights are a function of the parameters. Therefore, constraining the parameters ensures that the weights for past observations go to zero and that the further an observation is from the present, the faster the weight goes to zero.
Figure 19.6 Complete Specifications Tab
Modeling Options
Enables you to select or deselect the Constrain Parameters option.
Constrain Parameters
If selected, constrains the parameters in such a way that the further an observation is from the present, the less effect it has on the present state of the model. Constrain Parameters is selected by default.
Forecast Settings
Enables you to specify the following optional settings:
NAhead
Specifies the number of steps ahead to forecast. The number of steps must be nonnegative.
Period
Specifies seasonality values to be considered in the model fitting process. By default, the period is set to the suggested seasonality from the Analysis of Time Pattern report. If you want to consider models with different seasonality, specify the additional periods here and separate them with a comma. The period must be greater than zero.
Model Selection Strategy
Enables you to specify how the best model is chosen.
Information Criteria
Determines the best model based on the specified information criteria. The available information criteria are AIC and BIC.
Tip: Use BIC if the time series is long.
Forecasting Performance
Determines the best model based on a performance selection algorithm that involves a holdback set. First, the time series is partitioned into a training set and a holdback set. The value of NHoldback specifies the number of observations in the holdback set. Then, the algorithm fits all recommended or user-specified models on the data in the training set. Forecasts are made on the holdback set using the individual fitted models. These forecasts are compared to the actual holdback observations and the models are evaluated using the specified metric. The model with the best metric is selected for the final model. Last, the selected final model is fit to the entire time series (training set and holdback set) and the refitted model is used to forecast beyond the last observation of the time series.
Metric
Specifies the metric to evaluate the forecasts made by the individual model fits. The available metrics are Root Mean Square Error (RMSE), Mean Square Error (MSE), and Mean Absolute Error (MAE).
NHoldback
Specifies the number of observations used in the holdback set.
Other Options
Enables you to specify the following options:
Preserve Model Selection Criterion
Saves the model selection criterion for the set of models that is fit to the data. After model fitting, this information is shown in the Information Criterion of All Models for All Series report.
Forecast Interval Level
The prediction interval level for the forecasts. This changes the width of the shaded area in the forecasting plots.
Imputation for Applicable Models
Specifies the imputation method used during the model fitting process.
Note: These options change only the data that are used for model fitting. The raw data are not changed.
None
Does not impute missing values.
Last Value
Imputes missing values by using the last value that is available before a sequence of missing observations.
Middle Value
Imputes missing values by averaging the last value that is available before a sequence of missing observations and the first value that is available after a sequence of missing observations.
Linear Interpolation
Imputes missing values by creating a linear interpolation between the last value that is available before a sequence of missing observations and the first value that is available after a sequence of missing observations.
When you click Run, the specified set of models is fit. A progress bar appears that reports the number of active threads, the number of finished and total tasks, and the percentage of finished tasks. Note that a task is defined as the fitting of all specified models for one series and response variable combination. When the fitting process is complete, the Model Reports report is shown. See Time Series Forecast Model Reports. If you make any changes to the options in the Model Specifications report and click Run again, the Model Reports report is replaced with a new report.