User manual SPSS TRENDS 13.0

[. . . ] SPSS Trends 13. 0 ® For more information about SPSS® software products, please visit our Web site at http://www. spss. com or contact SPSS Inc. 233 South Wacker Drive, 11th Floor Chicago, IL 60606-6412 Tel: (312) 651-3000 Fax: (312) 651-3668 SPSS is a registered trademark and the other product names are the trademarks of SPSS Inc. No material describing such software may be produced or distributed without the written permission of the owners of the trademark and license rights in the software and the copyrights in the published materials. Use, duplication, or disclosure by the Government is subject to restrictions as set forth in subdivision (c) (1) (ii) of The Rights in Technical Data and Computer Software clause at 52. 227-7013. [. . . ] Leave the Start, Stop, and By text boxes with their default values of 0, 1, and 0. 1, respectively. The Grid Search option provides a convenient method for determining the best-fit model parameters by calculating goodness-of-fit measures for each of the grid values. The current selections result in values of alpha ranging from 0 to 1 in increments of 0. 1. The analysis is still performed for each of the points in the grid, but the output is limited to displaying results for the 10 best models. E Click Continue. E Click OK in the Exponential Smoothing dialog box. 56 Chapter 8 Figure 8-7 Exponential smoothing, no trend or seasonality The model output lists the 10 best-fitting values of alpha, along with the associated sums of squared errors (SSE) for each value. Each value of alpha corresponds to a different model, with models ranked according to their SSE value. A lower rank implies a smaller SSE and thus a model that gives a better fit to the data. The SSE measure of error is lowest when alpha is 0. 1, indicating that an alpha of 0. 1 gives the best fit to the data for this class of models. This low value of alpha indicates that the overall level of the series is best predicted when all observations have roughly equal weight. To see how well the simple model fits the data, you'll need to reopen the Sequence Charts dialog box. A convenient shortcut for reopening previous dialog boxes is as follows: E Click the Dialog Recall toolbar icon. E Select the entry for the desired dialog box, which in this case is Sequence Charts. 57 Exponential Smoothing Figure 8-8 Sequence Charts dialog box E Click Reset. This will restore the dialog box to its default settings, thus removing the timeline settings used previously. E Select men and FIT_1 and move them into the Variables list. E Click OK. 58 Chapter 8 Figure 8-9 Predictions from exponential smoothing, no trend or seasonality Notice that the model, as expected, does not account for the observed seasonality. In addition, it predicts an initial downward trend in contrast to the data, which exhibits a continuing upward trend. Examining the autocorrelations and partial autocorrelations for the residuals of the best-fit simple model provides more quantitative insight than viewing the sequence charts. Significant structure in either of these correlation functions would imply that the underlying model is incomplete. E From the menus choose: Graphs Time Series Autocorrelations. . . 59 Exponential Smoothing Figure 8-10 Autocorrelations dialog box E Select the error variable ERR_1 associated with the fit from the simple model. E Click OK. 60 Chapter 8 Figure 8-11 Residual autocorrelation plot for simple model The autocorrelation function shows a significant peak at a lag of 12. This is no surprise, since the simple model doesn't account for seasonality and there is a strong annual seasonal component in the data. 61 Exponential Smoothing Figure 8-12 Residual autocorrelation statistics for simple model Notice also that the Box-Ljung statistic at a lag of 12 is statistically significant. This underscores the fact that the lag 12 autocorrelation is significant and represents structure not accounted for in the present model. 62 Chapter 8 Figure 8-13 Residual partial autocorrelation plot for simple model The partial autocorrelation function removes the indirect effect of all intervening lags, providing the best measure of a direct relationship between time series values separated by a given lag. The partial autocorrelation function for the simple model shows the same significant peak at a lag of 12 as the autocorrelation function. This provides definitive proof that the residuals of the simple model contain the structure of the annual seasonality of the time series. Summary Given the poor fit of the simple model to the data and the presence of significant structure in the model's residuals, you can conclude that the simple model is not a good choice for modeling the data. [. . . ] When the regression does not contain an intercept term, refer to Farebrother's tabulated values of the "minimal bound" instead of Savin and White's lower bound dL. In this instance, the upper bound is the conventional bound dU found in the Savin and White tables. To test for positive first-order autocorrelation, use Farebrother's 179 Durbin-Watson Significance Tables Positive Serial Correlation tables. To test for negative first-order autocorrelation, use Farebrother's Negative Serial Correlation tables. [. . . ]