Assuming that the model in Example 38.2 is satisfactory, a seasonal adjustment that uses forecast extension can be performed by adding the X11 statement to the procedure. By default, the data is forecast one year ahead at the end of the series.
ods output D8A#1=SalesD8A_1; ods output D8A#2=SalesD8A_2; ods output D8A#3=SalesD8A_3; ods output D8A#4=SalesD8A_4; proc x12 data=sales date=date; var sales; transform power=0; arima model=( (0,1,1)(0,1,1) ); estimate; x11; run;
title 'Stable Seasonality Test'; proc print data=SalesD8A_1 LABEL; run;
title 'Nonparametric Stable Seasonality Test'; proc print data=SalesD8A_2 LABEL; run;
title 'Moving Seasonality Test'; proc print data=SalesD8A_3 LABEL; run;
title 'Combined Seasonality Test'; proc print data=SalesD8A_4 LABEL NOOBS; var _NAME_ Name1 Label1 cValue1; run;
Table D8A, which contains the seasonality tests, is shown in Output 38.3.1.
Output 38.3.1: Table D8A as Displayed
Test for the Presence of Seasonality Assuming Stability | |||||
---|---|---|---|---|---|
Sum of Squares | DF | Mean Square | F-Value | ||
Between Months | 23571.41 | 11 | 2142.855 | 190.9544 | ** |
Residual | 1481.28 | 132 | 11.22182 | ||
Total | 25052.69 | 143 |
Nonparametric Test for the Presence of Seasonality Assuming Stability |
||
---|---|---|
Kruskal-Wallis Statistic |
DF | Probability Level |
131.9546 | 11 | .00% |
Moving Seasonality Test | |||||
---|---|---|---|---|---|
Sum of Squares | DF | Mean Square | F-Value | ||
Between Years | 259.2517 | 10 | 25.92517 | 3.370317 | ** |
Error | 846.1424 | 110 | 7.692204 |
Summary of Results and Combined Test for the Presence of Identifiable Seasonality | |
---|---|
Seasonality Tests: | Probability Level |
Stable Seasonality F-test | 0.000 |
Moving Seasonality F-test | 0.001 |
Kruskal-Wallis Chi-square Test | 0.000 |
Combined Measures: | Value |
T1 = 7/F_Stable | 0.04 |
T2 = 3*F_Moving/F_Stable | 0.05 |
T = (T1 + T2)/2 | 0.04 |
Combined Test of Identifiable Seasonality: | Present |
The four ODS statements in the preceding example direct output from the D8A tables into four data sets: SalesD8A_1
, SalesD8A_2
, SalesD8A_3
, and SalesD8A_4
. It is best to direct the output to four different data sets because the four tables associated with Table D8A have varying
formats. The ODS data sets are shown in Output 38.3.2, Output 38.3.3, Output 38.3.4, and Output 38.3.5.
Output 38.3.2: Table D8A Output in Data Set SalesD8A_1
Stable Seasonality Test |
Obs | _NAME_ | FT_SRC | Sum of Squares | DF | Mean Square | F-Value | FT_AST |
---|---|---|---|---|---|---|---|
1 | sales | Between Months | 23571.41 | 11 | 2142.855 | 190.9544 | ** |
2 | sales | Residual | 1481.28 | 132 | 11.22182 | . | |
3 | sales | Total | 25052.69 | 143 | . | . |
Output 38.3.3: Table D8A Output in Data Set SalesD8A_2
Nonparametric Stable Seasonality Test |
Obs | _NAME_ | Kruskal-Wallis Statistic |
DF | Probability Level |
---|---|---|---|---|
1 | sales | 131.9546 | 11 | .00% |
Output 38.3.4: Table D8A Output in Data Set SalesD8A_3
Moving Seasonality Test |
Obs | _NAME_ | FT_SRC | Sum of Squares | DF | Mean Square | F-Value | FT_AST |
---|---|---|---|---|---|---|---|
1 | sales | Between Years | 259.2517 | 10 | 25.92517 | 3.370317 | ** |
2 | sales | Error | 846.1424 | 110 | 7.692204 | . |
Output 38.3.5: Table D8A Output in Data Set SalesD8A_4
Combined Seasonality Test |
_NAME_ | Name1 | Label1 | cValue1 |
---|---|---|---|
sales | Seasonality Tests: | Probability Level | |
sales | |||
sales | P_STABLE | Stable Seasonality F-test | 0.000 |
sales | P_MOV | Moving Seasonality F-test | 0.001 |
sales | P_KW | Kruskal-Wallis Chi-square Test | 0.000 |
sales | |||
sales | Combined Measures: | Value | |
sales | |||
sales | T1 | T1 = 7/F_Stable | 0.04 |
sales | T2 | T2 = 3*F_Moving/F_Stable | 0.05 |
sales | T | T = (T1 + T2)/2 | 0.04 |
sales | |||
sales | IDSeasTest | Combined Test of Identifiable Seasonality: | Present |