The X12 Procedure |

Assuming that the model in Example 32.2 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. Table D8.A is shown in Output 32.3.1.

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 D 8.A: F-tests for Seasonality

For variable sales

For variable sales

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 |

** Seasonality present at the 0.1 percent level.

Nonparametric Test for the Presence of Seasonality Assuming Stability |
||
---|---|---|

Kruskal-Wallis Statistic |
DF | Probability Level |

131.9546 | 11 | .00% |

Seasonality present at the one percent level.

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 |

**Moving seasonality present at the one percent level.

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 32.3.2, Output 32.3.3, Output 32.3.4, and Output 32.3.5.

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 |

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