What are seasonal adjustment, calendar day adjustment, and trend adjustment? How exactly do they work? How do they help uncover meaningful economic movement?
What does seasonal adjustment look for?
When measured (observed) at least four times a year, certain kinds of economic activity show patterns that recur year-to-year. Visually, such time series show peaks and troughs that (a) are regularly spaced, (b) have a consistent direction, and (c) are approximately the same magnitude each year relative to the trend. Such a time series can be decomposed into four components:
- The trend which describes long-term or secular change.
- Seasonal factors which are systematic and recurring; they are produced by natural conditions, business and administrative procedures, or social and cultural behavior.
- Calendar factors
- An irregular component which is unsystematic and short-term; such as a natural disaster, business upset or armed conflict.
A not seasonally adjusted series (a.k.a. NSA, unadjusted or original) is the sum of all four components. A seasonally adjusted series (a.k.a. SA or deseasonalized) is the sum of three components. The trend series (sometimes trend adjusted) is the remainder after all identifiable recurring components are removed. That is:
- NSA series = Trend + seasonal factors + calendar factors + irregular component
- SA series = Trend + calendar factors + irregular component
- Calendar day and seasonally adjusted (CDASA) series = Trend + irregular component
Are there other kinds of effect?
Calendar day effects (a.k.a. working day or trading day effects) change the amount of economic activity in a period (usually a calendar month) from one year to the next, for which calendar day adjustment (a.k.a. CDA or WDA) compensates. For example:
- The number of weekends in a given month
- The Easter holiday may fall in either March or April
Sports event effects pertain to major international sporting events that occur on a multiannual cycle, e.g., the Olympics or FIFA World Cup.
What kinds of dataset show seasonality?
For example:
- Home sales: In regions with winter, sales are higher in the spring. Conversely, Arizona's year-round warm weather reduces the seasonality.
- Retail sales: In countries that celebrate Christmas, retail sales are higher in November and December; in countries that celebrate the lunar new year, sales are higher in the spring.
How sources use adjustment
For example:
- The Australian Bureau of Statistics and Statistics New Zealand report many series in three variants: NSA, SA and Trend.
- European sources report many CDA series because movable holidays are common (more so than in the U.S. and Japan); it is possible to adjust for both calendar and seasonal effects.
- The Chinese New Year is a moving holiday on the 12-month Gregorian calendar, and China's National Bureau of Statistics responds by reporting January and February as a single period.
- Switzerland produces a variant of GVA that is adjusted for sports events.
How seasonal adjustment is performed
Seasonal adjustment is a mathematical process that analyzes a time series and identifies the seasonal and trend components. The original series must have a minimum length (usually three to five years).
Appending to the series will affect the seasonal factors that are extracted; consequently, SA series are subject to revision even if the underlying NSA history is immutable. That is, SA is an estimate based on observed behavior, and as more behavior is observed, the estimate will be refined.
The process of seasonal adjustment is performed by software, notably the X-11 suite (and its successors, X-12, X-13, X-13ARIMA-SEATS, etc.) developed by national statistical agencies over the past several decades. The programs are highly configurable to suit the nature of the data. (Note that the punctuation of the name varies between authors.)
Why not seasonally adjust everything?
Seasonal adjustment is inappropriate if the time series is dominated by trend or irregular components. In fact, application to a series that doesn't show seasonality may introduce an artificial seasonal element.
Are there alternatives to seasonal adjustment?
Year-over-year change is a partial analytic alternative, but it has shortcomings:
- Cannot identify turning points within a year
- Lag
- Ignores trading day effects
References
- At the U.S. Census Bureau:
- At Statistics Canada:
- At the Australian Bureau of Statistics:
See also
Updates to this article
- 7 Dec 2015 - Initial version.
- 12 Feb 2016
- 21 May 2021
- 6 Feb 2024 - Corrected component breakdown, added sports event effect, updated external and cross-reference links.