SAS/Ets User's Guide 229. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 2272 F Chapter 33 The X11 Procedure The F test for moving seasonality is performed by a two-way analysis of variance. The two factors are seasons months or quarters and years. The years effect is tested separately the null hypothesis is no effect due to years after accounting for variation due to months or quarters. For further details about the moving seasonality test see Lothian 1984a b 1978 and Higginson 1975 . The significance level reported in both the moving and stable seasonality tests are only approximate. Table D8 the Final Unmodified SI Ratios is constructed from an averaging operation that induces a correlation in the residuals from which the F test is computed. Hence the computed F statistic differs from an exact F statistic see Cleveland and Devlin 1980 for details. The test for identifiable seasonality is performed by combining the F tests for stable and moving seasonality along with a Kruskal-Wallis test for stable seasonality. The following description is based on Lothian and Morry 1978b other details can be found in Dagum 1988 1983 . Let Fs and Fm denote the F value for the stable and moving seasonality tests respectively. The combined test is performed as shown in Table and as follows 1. If the null hypothesis of no stable seasonality is not rejected at the significance level Ps then the series is considered to be nonseasonal. PROC X11 returns the conclusion Identifiable Seasonality Not Present. 2. If the null hypothesis in step 1 is rejected then PROC X11 computes the following quantities 3Fm t2 -m- Fs Let T denote the simple average of T1 and T2 T Ti T2 2 If the null hypothesis of no moving seasonality is rejected at the significance level Pm and if T the null hypothesis of identifiable seasonality not present is not rejected and PROC X11 returns the conclusion Identifiable Seasonality Not Present. 3. If the null hypothesis of identifiable seasonality not present has not been accepted but T1 T2 or the .
