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Home > Statistics > Explanatory Notes - Seasonal adjustment

Explanatory Notes - Seasonal adjustment


Technical details
Seasonally adjusting stock series



Seasonal adjustment aims to identify, estimate and remove regular seasonal fluctuations and typical calendar effects from time series data. Regular seasonal fluctuations are those movements which, on the basis of the past movements of the time series in question, can under normal circumstances be expected to recur with similar intensity in the same season each year. Calendar effects include effects caused by the number of working days or calendar days in the month, or the dates of particular occasions, such as Easter, within the year – the influence of such effects on a particular month can vary from year to year, but they can be quantified and adjusted.

An example of a seasonal series is the flow of credit card lending to individuals, where credit card lending tends to increase in December as consumers spend more in the run-up to Christmas. The non seasonally adjusted flows for credit card lending to individuals (red line below) show a seasonal peak in December followed by a seasonal trough in January. These can be explained by more spending in December and lower spending in January.

Data users are often interested in series which have been adjusted to remove seasonal effects, since these may give a better indication of the underlying movements. For those series where identifiable seasonality is detected, a seasonally adjusted version is also published.  The seasonally adjusted flows for credit card lending to individuals (blue line below), removes both the regular seasonal movements and any calendar effects.

 Chart for 'Flow of credit card lending to individuals'

Using seasonally adjusted data has a number of advantages over using the year-on-year movement of the non seasonally adjusted data. It is a more sophisticated process, and can succeed in the removal of calendar effects and better detection of turning points.

Comparability of data over time is enhanced through the application of seasonal adjustment methods. The Bank conducts regular reviews of the seasonal adjustment settings of its data series to ensure these remain satisfactory. 

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Technical details

The Bank of England seasonally adjusts its data using X-13ARIMA-SEATS.  The Bank uses the X-12-ARIMA functionality within this package.
The Bank seasonally adjusts approximately 400 published series, the majority being of monthly periodicity. The following considerations are taken into account when adjusting a series:


  • Type: Flows series that are derived from levels (stocks) series are not seasonally adjusted directly, but are instead derived from the seasonally adjusted levels series as described below. And the treatment for seasonally adjusting a levels series differs slightly to that for seasonally adjusting a pure flows series;
  • Frequency: Where possible, the seasonally adjusted quarterly series are derived from the corresponding seasonally adjusted monthly series, but in some cases the monthly equivalent is not available or is only available over a very short time span, in which case the quarterly series is seasonally adjusted directly;
  • Length: X-13ARIMA-SEATS requires a minimum of three years of data to seasonally adjust though a longer span of data is preferred to obtain reliable results;
  • Detection of seasonality: Before seasonally adjusting, various diagnostics are examined to decide whether the series requires seasonal adjustment. Footnotes are placed on series that do not show sufficient seasonality to indicate that they have been considered for seasonal adjustment, but are currently not seasonal;
  • Aggregation considerations: Aggregate time series can be adjusted directly or indirectly, as a sum of their components. The method chosen is whichever is shown to give a better seasonal adjustment of the total aggregate.
When the seasonal adjustment of a particular series is being reviewed, the Bank considers various diagnostic tests to assess the quality of potential seasonal adjustment to ensure that the final seasonal adjustment is of as high a quality as possible. Some series may be reviewed more frequently.

The Bank conducts annual reviews (split into three separate phases each year) of the settings used for seasonal adjustment of published series, and publishes the results in Bankstats (see list of References).  Any significant methodological changes are also documented.
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Seasonally adjusting stock series

Some monetary statistics series are reported naturally as flows (e.g. number of mortgage approvals for house purchase) and they should be seasonally adjusted as flows in their own right. Other flows series, however, are initially compiled in terms of amounts outstanding at the end-month reporting dates. These levels (or stocks) series are on a point in time basis, and for these series, users may also be interested in the derived flows and growth rates (see the “Changes, flows, growth rates” explanatory notes for further information on how these are derived). For such series, both seasonally adjusted levels and flows are derived by first seasonally adjusting a break-adjusted levels series (see also “Break-adjusted levels data”). The diagram below provides details of how these calculations work.

Image of diagram providing details of how seasonally adjusted stock series are calculated

    1. The break-adjusted ratio series[1]bt is used to temporarily adjust the NSA levels series to provide a break-adjusted series.
    2. This break-adjusted series is modelled (calendar effects estimates, outliers/level shifts corrected, forecasts generated) using the RegARIMA time series model component. Note that a multiplicative decomposition is used, i.e. a log transformation is performed.
    3. This linearised time series is fed in to the X-11 algorithm which estimates the components, including the seasonal component, using moving averages.
    4. The seasonally adjusted level, Lt, is found by dividing the break-adjusted series by the seasonal factor (and calendar factors) and then reversing the ratio adjustments by multiplication.[2]
    5. The seasonally adjusted flow series is calculated by using the formula shown. 
      [1] If the underlying series is naturally reported as a flow series then ratio time series are not required.
      [2] For conventional flow time series, this series is the final seasonally adjusted flow.

This method has a number of advantages over the alternative method (which is to seasonally adjust the break-adjusted NSA flows time series), including: (i) a multiplicative decomposition model can be used i.e. with the alternative method, an additive model must be used; and (ii) generally a larger degree of volatility in the unadjusted flows can make it difficult for the seasonal component to be identified and estimated.

Example X-13ARIMA-SEATS specification (spec) file

Below is an example of a X-13ARIMA-SEATS command file (“spec” file) that may be used to adjust a levels time series. In this example, a user-defined levels trading day regressor file is being used. Note that other settings – such as the use of additional regressor files, using distinct seasonal moving averages for individual months - may also be used in practice. 

Image of an example of a X-12-ARIMA command file (“spec” file)
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Key Resources

 Seasonal adjustment: 2014 update, Hussain, F & Meader, R (2014), Bankstats (Monetary & Financial Statistics), June 2014

 Modifications to the seasonal adjustment of M4 and M4 lending excluding intermediate OFCs measures, Berar, R & Meader, R (2013), Bankstats (Monetary & Financial Statistics), October 2013
 Seasonal adjustment: results of 2012 annual review, Meader, R (2013), Bankstats (Monetary & Financial Statistics), May 2013
 Seasonal adjustment: effects of the 2012 Diamond Jubilee, Owladi, J (2013), Bankstats (Monetary & Financial Statistics), January 2013
 Seasonal adjustment: 2012 update, Broughton, E & Owladi, J (2012), Bankstats (Monetary & Financial Statistics), May 2012
 Changes to the annual seasonal adjustment review, Hussain, F (2011),Bankstats (Monetary & Financial Statistics), March 2011
Seasonal Adjustment of M4 excluding intermediate OFCs (M4ex) - an update, Gilhooly, R & Hussain, F (2010), Bankstats (Monetary & Financial Statistics), November 2010
 Seasonal Adjustment of quarterly M4 excluding intermediate OFCs (M4ex), Hussain, F & Maitland-Smith, F (2010),Bankstats (Monetary & Financial Statistics), September 2010
 Seasonal Adjustment: 2010 annual review, Hussain, F & Shah, A (2010), Monetary and Financial Statistics, April 2010

 Seasonal Adjustment: 2009 annual review, Owladi, J & Hussain, F (2009), Monetary and Financial Statistics, April 2009

Seasonal Adjustment: 2008 annual review, Burgess, S (2008), Monetary and Financial Statistics, April 2008

Change in policy regarding the seasonal adjustment of quarterly series, Burgess, S (2007),Monetary and Financial Statistics, April 2007
Seasonal adjustment of UK monetary aggregates: direct versus indirect approach, Burnett, M (2006), Monetary and Financial Statistics, February 2006

 The treatment of securitisations and loan transfers when seasonally adjusting using X-12-ARIMA, Daines, M (2006), Monetary and Financial Statistics, March 2006
 Seasonal adjustment of monetary data: annual review, Daines, M (2005), Monetary and Financial Statistics, April 2005
 Historical comparison of seasonally adjusted series using GLAS and X-12-ARIMA, Daines, M (2004), Monetary and Financial Statistics, January 2004
Prospective change in seasonal adjustment methodology: consultation with users: summary of responses, Bank of England (2003), Monetary and Financial Statistics, February 2003 

Change in seasonal adjustment method to X-12-ARIMA, Thorp, J (2003), Monetary and Financial Statistics, December 2003
 Prospective change in seasonal adjustment methodology: consultation with users, Bank of England (2002), Monetary and Financial Statistics, November 2002
 Seasonal adjustment of UK monetary aggregates (QB 1996 Q2) p.209, Bianchi, M (1996), Quarterly Bulletin, 1996 Q2