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Statistics published by the Australian Bureau of Statistics (ABS) are usually presented at more than one level of detail. For example, Employment statistics are published for Males and Females and also for Persons, separate estimates are given for Juniors and Adults, Full time and Part time, State employment figures are published and an Australia total number is also given. When the finer level original estimates are added up, the results will be consistent with the published subtotal and total series (except possibly for slight discrepancies due to rounding).
In addition to original data, ABS publications often contain seasonally adjusted estimates. Seasonally adjusted estimates are calculated using the X11-based seasonal adjustment methodology which involves the adjustment of time series individually rather than jointly adjusting a number of time series as a set. As a consequence of this series-by-series adjustment procedure, there are two alternative methods that can be used to obtain seasonally adjusted subtotal and total series.
The first method consists of directly seasonally adjusting the subtotal and total series and is called direct seasonal adjustment. The second method involves seasonally adjusting each of the component series that contribute to a subtotal or total series, and then adding up the seasonally adjusted components to get a seasonally adjusted estimate at the higher level. The second method is called indirect or aggregative seasonal adjustment. The two methods do not produce the same seasonally adjusted series. This paper discusses the problem of how to select the method which produces the best adjustment.
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