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Seasonal adjustment is a statistical method for removing the seasonal variations of a time series that is used when analyzing non-seasonal trends. It is normal to report seasonally adjusted data for unemployment rates to reveal the underlying trends in labor markets.[1] Many economic phenomena have seasonal cycles, such as agricultural production and consumer consumption, e.g. greater consumption leading up to Christmas. It is necessary to adjust for this component in order to understand what underlying trends are in the economy and so official statistics are often adjusted to remove seasonal components. [2]

## Time series componentsEdit

Main article: Decomposition of time series

The investigation of many economic time series becomes problematic due to seasonal fluctuations. Time series are made up of four components:

• St: The seasonal component
• Tt: The trend component
• Ct: The cyclical component
• It: The error, or irregular component.

Unlike the trend and cyclical components, seasonal components, theoretically, happen with similar magnitude during the same time period each year. The seasonal components of a series are often considered to be uninteresting in their own right and to cause the interpretation of a series to be ambiguous. By removing the seasonal component, it is easier to focus on other components.[3]

Different statistical research groups have developed different methods of seasonal adjustment, for example X-12-ARIMA developed by the United States Census Bureau;[citation needed] TRAMO/SEATS developed by the Bank of Spain;[citation needed] and STAMP developed by a group led by S. J. Koopman.[citation needed] Each group provides software supporting their methods. Some versions are also included as parts of larger products, and some are commercially available. For example, SAS includes X-12-ARIMA, while Oxmetrics includes STAMP. A recent move by public organisations to harmonise seasonal adjustment practices has resulted in the development of Demetra+ by Eurostat and National Bank of Belgium which currently includes both X-12-ARIMA and TRAMO/SEATS.[citation needed]

## ExampleEdit

One famous example is the rate of unemployment which is also presented by a time series. This rate depends particularly on seasonal influences, which is why it is important to free the unemployment rate of its seasonal component. As soon as the seasonal influence is removed from this time series, the real trend of the unemployment rate is visible. Seasonal adjustment is mostly used in the official statistics implemented by statistical software like Demetra+.

When seasonal adjustment is not performed with monthly data, year-on-year changes are utilised in an attempt to avoid contamination with seasonality.

## Moves to standardise seasonal adjustment processesEdit

Due to the various seasonal adjustment practices by different institutions, a group was created by Eurostat and the European Central Bank to promote standard processes. In 2009 a small group composed of experts from European Union statistical institutions and central banks produced the ESS Guidelines on Seasonal Adjustment, which is being implemented in all the European Union statistical institutions. It is also being adopted voluntarily by other public statistical institutions outside the European Union.