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Model Viewer

In the Develop Models window, select the row in the table containing the Linear Trend model so that this model is highlighted. The model list should now appear as shown in Display 23.38.

Note that the Linear Trend model is now highlighted, but the Forecast Model column still shows the Double Exponential Smoothing model as the model chosen to produce the final forecasts for the series. Selecting a model in the list means that this is the model that menu items such as View Model, Delete, Edit, and Refit will act upon. Choosing a model by clicking its check box in the Forecast Model column means that this model will be used by the Produce Forecasts process to generate forecasts.

Now bring up the Model Viewer by clicking the right icon under the Browse button, or by selecting Model Predictions in the tool bar or the View pull-down menu. The Model Viewer displays the Linear Trend model, as shown in Display 23.39.

This graph shows the linear trend line representing the model predicted values together with a plot of the actual data values, which fluctuate about the trend line.

Prediction Error Plots

Select the second icon from the top in the vertical tool bar in the Model Viewer window. This switches the Viewer to display a plot of the model prediction errors (actual data values minus the predicted values), as shown in Display 23.40.

If the model being viewed includes a transformation, prediction errors are defined as the difference between the transformed series actual values and model predictions. You can choose to graph instead the difference betwen the untransformed series values and untransformed model predictions, which are called model residuals. You can also graph normalized prediction errors or normalized model residuals. Use the Residual Plot Options submenu under the Options pull-down menu.

Autocorrelation Plots

Select the third icon from the top in the vertical tool bar. This switches the Viewer to display a plot of autocorrelations of the model prediction errors at different lags, as shown in Display 23.41. Autocorrelations, partial autocorrelations, and inverse autocorrelations are displayed, with lines overlaid at plus and minus two standard errors. You can switch the graphs so that the bars represent significance probabilities, by selecting the Correlation Probabilities item on the tool bar or under the View pull-down menu. For more information on the meaning and use of autocorrelation plots, refer to Chapter 7, "The ARIMA Procedure,".

White Noise and Stationarity Plots

Select the fourth icon from the top in the vertical tool bar. This switches the Viewer to display a plot of white noise and stationarity tests on the model prediction errors, as shown in Display 23.42.

The white noise test bar chart shows significance probabilities of the Ljung-Box Chi Square statistic. Each bar shows the probability computed on autocorrelations up to the given lag. Longer bars favor rejection of the null hypothesis that the prediction errors represent white noise. In this example they are all significant beyond the .001 probability level, so that we reject the null hypothesis. In other words, the high level of significance at all lags makes it clear that the linear trend model is inadequate for this series.

The second bar chart shows significance probabilities of the Augmented Dickey-Fuller test for unit roots. For example, the bar at lag three indicates a probability of .0014, so that we reject the null hypothesis that the series is nonstationary. The third bar chart is similar to the second except that it represents the seasonal lags. Since this series has a yearly seasonal cycle, the bars represent yearly intervals.

You can click on any of the bars to display an interpretation. Click on the fourth bar of the middle chart. This displays the Recommendation for Current View, as shown in Display 23.43. This window gives an interpretation of the test represented by the bar clicked on: It is significant, therefore a stationary series is likely. It also gives a recommendation: You do not need to perform a simple difference to make the series stationary.

Parameter Estimates Table

Select the fifth icon from the top in the vertical tool bar to the right of the graph. This switches the Viewer to display a table of parameter estimates for the fitted model, as shown in Display 23.44.

For the linear trend model, the parameters are the intercept and slope coefficients. The table shows the values of the fitted coefficients together with standard errors and t-tests for the statistical significance of the estimates. The model residual variance is also shown.

Statistics of Fit Table

Select the sixth icon from the top in the vertical tool bar to the right of the table. This switches the Viewer to display a table of statistics of fit computed from the model prediction errors, as shown in Display 23.45. The list of statistics displayed is controlled by selecting Statistics of Fit from the Options pull-down menu.

Changing to a Different Model

Select the first icon from the top in the vertical tool bar to the right of the table to return the display to the predicted and actual values plots (Display 23.39).

Now return to the Develop Models window, but do not close the Model Viewer window. You can use the Next Viewer icon in the tool bar or your system's window manager controls to switch windows. You can resize the windows to make them both visible.

Select the Double Exponential Smoothing model so that this line of the model list is highlighted. The Model Viewer window is now updated to display a plot of the predicted values for the Double Exponential Smoothing model, as shown in Display 23.46. The Model Viewer is automatically updated to display the currently selected model, unless you specify Unlink (the third icon in the window's horizontal tool bar).

Forecasts and Confidence Limits Plots

Select the seventh icon from the top in the vertical tool bar to the right of the graph. This switches the Viewer to display a plot of forecast values and confidence limits, together with actual values and one-step-ahead within-sample predictions, as shown in Display 23.47.

Data Table

Select the last icon at the bottom of the vertical tool bar to the right of the graph. This switches the Viewer to display the forecast data set as a table, as shown in Display 23.48.

To view the full data set, use the vertical and horizontal scroll bars on the data table or enlarge the window.

Closing the Model Viewer

Other features of the Model Viewer and Develop Models window are discussed later in this book. For now, close the Model Viewer window and return to the Time Series Forecasting window.

To close the Model Viewer window, select Close from the window's horizontal tool bar or the File pull-down menu.

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