Why can I get the annual total by summing the seasonally adjusted monthly values or by summing the annual rates for each month or quarter of the year and dividing by 12 or 4?
When seasonal adjustment is done by dividing the time series by seasonal factors (or combined seasonal-trading day-holiday factors) it is arithmetically impossible for the adjusted series to have the same annual totals as the unadjusted series (except in the uninteresting case in which the time series values repeat perfectly from year to year). “Benchmarking” procedures can be used to modify the adjusted series so as to force the adjusted series to have the same totals as the unadjusted series, but these procedures do not account for evolving seasonal effects or for trading day differences due to the differing weekday compositions of different years.
Related Questions
- Why can I get the annual total by summing the seasonally adjusted monthly values or by summing the annual rates for each month or quarter of the year and dividing by 12 or 4?
- Why can I get the annual total by summing the seasonally adjusted monthly values (or by summing the annual rates for each month (quarter) of the year and dividing by 12 (4))?
- What is an annual rate? Why are seasonally adjusted data often shown as annual rates?
