Further details about seasonal adjustment data

Seasonal adjustment aims to identify, estimate and remove regular seasonal fluctuations and typical calendar effects from time series data.


Seasonal adjustment is a statistical technique which aims to identify, estimate and remove seasonal fluctuations and typical calendar effects (such as those caused by monthly variations in the number of trading days) from non-seasonally adjusted (NSA) time series data, making it easier for users to interpret this data and compare it with that from a prior period. Seasonal effects are seasonal fluctuations that, under normal circumstances, can be expected to recur with similar intensity in the same season each year, e.g. variations in economic activity due to Christmas holidays, or weather patterns. Calendar effects include effects caused by the composition of the calendar, e.g. due to differing number of working or calendar days in the month, or the dates of particular occasions, such as Easter holiday days, 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 number of total sterling approvals for house purchase to individuals. This series shows clear seasonal troughs in December and January (see aqua line below). However, data users are often interested in the underlying movements of the series rather than any seasonal effects. The seasonally adjusted series for the number of total sterling approvals for house purchase to individuals (see orange line below) has both the seasonal and calendar effects removed.

Chart 1: Number of mortgage approvals

The Bank conducts regular reviews of the seasonal adjustment settings of its data series to ensure these remain satisfactory. 

Technical details

The Bank of England seasonally adjusts its data using X-13ARIMA-SEATS.

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. The treatment for seasonally adjusting a levels series differs slightly to that for a 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 more reliable results;
  • Detection of seasonality: Before seasonally adjusting, the results of various diagnostics are examined to decide whether the series actually requires seasonal adjustment.
  • Aggregation considerations: Aggregate time series can be directly or indirectly seasonally adjusted. In the latter case, component series will be seasonally adjusted individually and the seasonally adjusted data aggregated as a sum of their components. The decision to use indirect or direct seasonal adjustment is a complex and carefully balanced judgement, but generally, the method that results in a more optimal seasonal adjustment is preferred.

Some series may be reviewed more frequently than others.

The Bank conducts regular reviews of the settings used for seasonal adjustment of published series, and publishes the results via a Statistical article. Any significant methodological changes are also documented. During the monthly statistical production cycle additive outliers are identified and, given time and resource constraints within the production cycle, implemented if they would change the seasonal adjustment sufficiently to change the economic story of the data. If they are found to not significantly alter the economic story presented in the seasonally adjusted series, these outliers will be implemented after the current monthly statistical production round has concluded, but ahead of the next one.

Seasonally adjusting stock series

Some monetary statistics series are reported naturally as flows (e.g. the 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). 

Figure 1: The seasonal adjustment process for flows and levels

If the underlying data of the series is collected as flow data, then no transformations prior or post seasonal adjustment are required to obtain a seasonally adjusted flow series. However, if the underlying data of the series is collected using stock data, then the following steps occur to obtain the seasonally adjusted flow series:

  1. The non-seasonally adjusted level series, \[U_t\], is transformed into a break-adjusted non-seasonally adjusted series using a ratio series, \[b_t\], is used to temporarily adjust the non-seasonally adjusted level series.
  2. Seasonal adjustment is performed on the non-seasonally adjusted level series resulting in the seasonally adjusted break-adjusted series, \[V_t\]. Note that a multiplicative decomposition is used, i.e. a log transformation is performed.
  3. The seasonally adjusted level series, \[L_t\], is found by multiplying the seasonally adjusted break-adjusted series, \[V_t\], by the ratio series, \[b_t\].
  4. The seasonally adjusted flow series is calculated by multiplying the ratio of the prior and current periods of the ratio series, \[\frac{b_{t-1}}{b_t}\], with the seasonally adjusted level series, \[L_t\], and finally subtracting the seasonally adjusted level series of the previous period, \[L_{t-1}\].

The main benefit of this method over the alternative method (which is to seasonally adjust the break-adjusted NSA flows time series), is that a multiplicative decomposition model can be used instead of an additive model.

Further information

Seasonal adjustment: 2022 Covid-19 Review, Haarmann, J (2022) Statistics article, August 2022
Seasonal adjustment 2018 update, Brown, M (2018) Statistics article, June 2018
Seasonal adjustment 2017 update, Taylor, K (2017) Statistics article, May 2017
Seasonal adjustment: 2016 update, Boobier, T (2016) Statistics article, June 2016
Seasonal adjustment: 2015 update, Meader, R (2015) Statistics article, June 2015
Seasonal adjustment: 2014 update, Hussain, F & Meader, R (2014) Statistics article, June 2014
Modifications to the seasonal adjustment of M4 and M4 lending excluding intermediate OFCs measures, Berar, R & Meader, R (2013), Statistics article, October 2013
Seasonal adjustment: results of 2012 annual review, Meader, R (2013), Statistics article, May 2013
Seasonal adjustment: effects of the 2012 Diamond Jubilee, Owladi, J (2013), Statistics article, January 2013
Seasonal adjustment: 2012 update, Broughton, E & Owladi, J (2012), Statistics article, May 2012
Changes to the annual seasonal adjustment review, Hussain, F (2011), Statistics article, March 2011
Seasonal Adjustment of M4 excluding intermediate OFCs (M4ex) - an update, Gilhooly, R & Hussain, F (2010), Statistics article, November 2010
Seasonal Adjustment of quarterly M4 excluding intermediate OFCs (M4ex) , Hussain, F & Maitland-Smith, F (2010), Statistics article, September 2010
Seasonal Adjustment: 2010 annual review, Hussain, F & Shah, A (2010), Statistics article, April 2010
Seasonal Adjustment: 2009 annual review, Owladi, J & Hussain, F (2009), Statistics article, April 2009
Seasonal Adjustment: 2008 annual review, Burgess, S (2008), Statistics article, April 2008 
Change in policy regarding the seasonal adjustment of quarterly series, Burgess, S (2007), Statistics article, April 2007
Seasonal adjustment of UK monetary aggregates: direct versus indirect approach, Burnett, M (2006), Statistics article, February 2006 
The treatment of securitisations and loan transfers when seasonally adjusting using X-12-ARIMA,  Daines, M (2006), Statistics article, March 2006
Seasonal adjustment of monetary data: annual review, Daines, M (2005), Statistics articleMonetary and Financial Statistics, April 2005
Historical comparison of seasonally adjusted series using GLAS and X-12-ARIMA, Daines, M (2004), Statistics article, January 2004
Prospective change in seasonal adjustment methodology: consultation with users: summary of responses, Bank of England (2003), Statistics article, February 2003
Change in seasonal adjustment method to X-12-ARIMA, Thorp, J (2003), Statistics article, December 2003
Prospective change in seasonal adjustment methodology: consultation with users, Bank of England (2002), Statistics article, November 2002
Seasonal adjustment of UK monetary aggregates (QB 1996 Q2) p.209, Bianchi, M (1996), Quarterly Bulletin, 1996 Q2.

This page was last updated 20 March 2024