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Seasonal adjustment

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Title: Seasonal adjustment  
Author: World Heritage Encyclopedia
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Subject: Seasonality, Decomposition of time series, BV4.1 (software), Economic data, Statistics
Collection: Seasonality
Publisher: World Heritage Encyclopedia

Seasonal adjustment

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 1
  • Seasonal adjustment 2
  • Example 3
  • Moves to standardise seasonal adjustment processes 4
  • Use of seasonally adjusted data in regressions 5
  • Shortcomings of using seasonally adjusted data 6
  • See also 7
  • References 8
  • Further reading 9
  • External links 10

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]

Seasonal adjustment

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 Demetra+ by Eurostat and National Bank of Belgium which currently includes both X-12-ARIMA and TRAMO/SEATS.[7]


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 to school graduates or dropouts 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]

See also


  1. ^
  2. ^ "Retail spending rise boosts hopes UK can avoid double-dip recession".  
  3. ^
  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. ^
  9. ^ Maddala, G. S.; Kim, In-Moo (1998). Unit Roots, Cointegration, and Structural Change. Cambridge: Cambridge University Press. pp. 364–365.  
  10. ^ Hyndman, Rob J; Athanasopoulos, George. "Forecasting: principles and practice". Retrieved 20 May 2015. 

Further reading

  • Enders, Walter (2010). Applied Econometric Time Series (Third ed.). New York: Wiley. pp. 97–103.  
  • Hylleberg, Svend (1986). Seasonality in Regression. Orlando: Academic Press. pp. 36–44.  

External links

  • Download Demetra+ from
  • Seasonal adjustment at CROS portal (
  • ESS Guidelines on Seasonal Adjustment
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