Seasonal adjustment is a statistical method for removing the seasonal component of a time series that exhibits a seasonal pattern. It is usually done when wanting to analyse the trend of a time series independently of the seasonal components. 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 components

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.

The difference between seasonal and cyclic patterns:

• Seasonal patterns have a fixed and known length, while cyclic patterns have variable and unknown length.
• The average length of a cycle is usually longer than that of seasonality.
• The magnitude of cyclic variation is usually more variable than that of seasonal variation. [3]

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 sometimes considered to be uninteresting and to hinder the interpretation of a series. Removing the seasonal component directs focus on other components and will allow better analysis.[4]

Different statistical research groups have developed different methods of seasonal adjustment, for example X-12-ARIMA developed by the United States Census Bureau; TRAMO/SEATS developed by the Bank of Spain;[5] and STAMP developed by a group led by S. J. Koopman.[6] 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.[7]

## Example

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. Such seasonal influences can be due school leavers looking to enter into the workforce and regular fluctuations during holiday periods. Once the seasonal influence is removed from this time series, the unemployment rate data can be meaningfully compared across different months and predictions for the future can be accurately forecast.[8] Seasonal adjustment is 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 processes

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.

## Use of seasonally adjusted data in regressions

By the Frisch–Waugh–Lovell theorem it does not matter whether dummy variables for all but one of the seasons are introduced into the regression equation, or if the independent variable is first seasonally adjusted (by the same dummy variable method), and the regression then run.

Since seasonal adjustment introduces a "non-revertible" moving average (MA) component into time series data, unit root tests (such as the Phillips–Perron test) will be biased towards non-rejection of the unit root null.[9]

## Shortcomings of using seasonally adjusted data

Use of seasonally adjusted time series data can be misleading. This is because the seasonally adjusted series contains both the trend-cycle component and the error component. As such, the seasonally adjusted data will not be "smooth" and what appears to be "downturns" or "upturns" may actually be randomness in the data. For this reason, if the purpose is finding turning points in a series, it is better to use the trend-cycle component rather than the seasonally adjusted data.[10]

## References

1. ^ http://www.bls.gov/cps/seasfaq.htm
2. ^
3. ^ https://www.otexts.org/fpp/2/1
4. ^ FAQs on Seasonal Adjustment
5. ^ OECD Glossary: Seasonal Adjustment
6. ^ STAMP Modelling and Forecasting
7. ^ OECD, Short-Term Economic Statistics Expert Group (June 2002), Harmonising Seasonal Adjustment Methods in European Union and OECD Countries
8. ^ https://www.otexts.org/fpp/6/1
9. ^ Maddala, G. S.; Kim, In-Moo (1998). Unit Roots, Cointegration, and Structural Change. Cambridge: Cambridge University Press. pp. 364–365. ISBN 0-521-58782-4.
10. ^ Hyndman, Rob J; Athanasopoulos, George. "Forecasting: principles and practice". Retrieved 20 May 2015.