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Although a preliminary analysis has shown that there was no evidence of any consistent seasonal behavior, some seasonal models were evaluated over the months 49 to 60 inclusive of the test period. The BoxJenkins AR (1) model, which was the best of that class of models for the largest number of items, 6 out of 10, was compared with a seasonal AR(1) model for the months of the test period. The nonseasonal model gave lower sums of squared errors for 6 of the 10 items and gave a lower sum of root mean squared errors over all 10 items. The results are shown in Table 8.
Items  SSE (AR1)  SSE (seasonal AR1)  FStatistics (larger SSE being the numerator)  RMSE (AR1)  RMSE (seasonal AR1) 

SAV740  74472  75618  1.015  78.78  79.38 
SAV091  5273  5395.2  1.023  20.96  21.20 
SAV763  13015904  12677014  1.027  1140.87  1125.52 
SAV012  2242976  1196782  1.874  432.34  315.80 
REM061  2208355  1865122  1.184  428.99  394.24 
SAV739  89181  93241  1.046  86.21  88.15 
CUA085  941180  1042557  1.108  280.06  294.75 
SAV013  3308384  2692286  1.229  525.07  473.66 
CUA778  10444654  14970750  1.433  932.95  1116.94 
REM037  3327895  3674954  1.104  526.62  553.40 
5 % Critical Region, F>2.69  SUM= 4452.85  SUM= 4463.04 
Because of this result, no further analysis was conducted with seasonal BoxJenkins models. It was found that the HoltWinters seasonal model gave better forecasts for the test period than the Holt's model. There was a reduction of around 10% in the sum of the root mean squared errors over the 10 items in the sample. This does not necessarily indicate that there is after all consistent seasonality in the demand over time. It is well known that a large outlier value for a month in one of the initial years of setting up the HW model can lead to a significant "seasonal" factor being produced for that month, which can take several years to disappear in the usual updating process. The greater number of parameters in the HoltWinters method compared to Holt's alone can in some circumstances take out some of the outlier values and exclude their effect from the updating of the underlying level and trend. It was decided therefore to research the effect of including the HoltWinters in place of the Holt model in the earlier analysis.
The results of these analyses are summarized in Table 9, in the same format as for Table 7. The use of the "seasonal" HoltWinters model gives a reduction of about 10% in the sum of the root mean squared errors compared to the Holt's model. The value is thus about the same as obtained with the best of the combination of nonseasonal forecasting models. More importantly, the same reduction of 10% in the sum of the root mean squared errors occurs for every weighting method, as can be seen by comparing the entries in Tables 7 and 9 row by row. The relative rankings of the various weighting methods is very similar to that found in Table 7. The only minor difference is the relatively poorer performance of the Fixed Common Weights over the four forecasting methods. The new hybrid method again gives the best performance, saving around 10% compared with using the HoltWinters method alone.
FORECASTS  WEIGHTS  Sum of Root Mean Squared Errors  Percentage Saving on HoltWinters 

HoltWinters  3900  
Best over Past Year  3652  6.4%  
Four Common Methods  Fixed Common  3767  3.4% 
Four Common Methods  Individual Fixed  3553  8.9% 
Individual Rolling  3626  7.1%  
Hybrid  3507  10.1%  
Individual Three  Individual Fixed  3558  8.8% 
Best Methods  Individual Rolling  3576  8.3% 
Hybrid  3527  9.6% 
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