National accountsQ2 2014


About seasonal adjustment

General information on seasonal adjustment

What is seasonal adjustment?

Monthly and quarterly time series are often characterised by considerable seasonal variations, which might complicate inter-period comparability. Such time series are therefore subjected to a process of seasonal adjustment in order to remove the effects of seasonal fluctuations. Once data have been adjusted for seasonal effects by X-12-ARIMA or some other seasonal adjustment tool, a clearer picture of the time series emerge.

For more information on seasonal adjustment, please refer to Statistics Norway’s: metadata on methods: seasonal adjustment .

Why seasonally adjust these statistics?

Because of climatic conditions, public holidays and holidays in July and December, the intensity of the production varies throughout the year. The same applies to household consumption and other parts of the economy.

This makes a direct comparison of two consecutive quarters difficult. In order to adjust for these conditions, the quarterly national accounts are seasonally adjusted which makes it possible to conduct an analysis of the underlying change in economic activity between periods.

It is important to mention some factors of the seasonally adjustment of the QNA which has to be given specific attention compared to other short time economic indicators:

  • The series for the main aggregates in the QNA is a result of aggregation of many components where the properties of the components are not homogenous.
  • Statistics Norway has chosen that consistency between the components and the main aggregates also applies to the seasonally adjusted series to make it easy to identify which series contribute the most to the results.
  • In many cases it may be difficult to identify the seasonal-/calendar effects. This is a general phenomenon for quarterly series – especially when the series cover the whole country.
  • The QNA-series are often estimated through monthly economic indicators. It is important that the results of the seasonal adjustments are fairly similar.

All of these factors lead to larger flexibility and variation in the methods and routines for the seasonal adjustment of QNA-series than what is common for other statistics.

New method from the 3rd quarter of 2011.

From the 3rd quarter of 2011 QNA was published according to the new standard for industrial classification. We used this opportunity to change some routines regarding seasonal adjustment to ease the dissemination of constant price figures. In addition, there has been a significant reduction in the number of seasonally adjusted time series.

Background information

  • The QNA uses the final national accounts year as the base year for calculating “new” quarters. This means for example that when we use 2009 as the base year in November, it will be used to calculate the quarterly figures at constant prices for all quarters from the 1st quarter of 2010 to the 2nd quarter of 2012. When we calculate the 3rd quarter of 2012, the base year will be changed to 2010, and the quarters in 2011 and 2012 will be updated to the new base year.
  • For all quarters compiled on the basis of the base year, we have figures that are additive. That means that we can add together individual series in constant prices to get the correct aggregate.
  • The annual accounts always have t-1 as the base year, and this is the reference to calculate volume growth.
  • The annual growth rates estimated at t-1 prices will be kept and therefore we chain growth rates in the prices of the reference year (which is the current base year in the QNA).
  • Chaining is done on all levels and this means that additivity no longer applies. Thus, we can not add together figures for value added at constant prices and get the GDP at constant prices for quarters that are “older” than the base year.
  • The quarterly figures are always benchmarked against the annual figures. The QNA are updated with a new base year every year (i.e. the latest final version of the annual accounts). Every time we change base year (reference year), the recalculation of the quarterly accounts is carried out by distributing the annual figures between the quarters using the original quarterly figures as keys. The recalculated quarterly accounts will then add up to the annual accounts at constant and current prices. The harmonisation is based on the principle that the differences between the quarterly changes to the original and harmonised series shall be as small as possible. The quarterly accounts should add up to the figures in the annual accounts.
  • Chaining in the QNA is done every year and the further we are from the reference price year, the greater the so-called chaining effect will be.
  • To seasonally adjust the GDP (and all other aggregates) we used an indirect method. This is done in order to be able to explain the contributions to GDP-growth, and consensus is that this is the preferred method for this kind of data. Please see chapter below for more details on the direct vs. indirect approach to seasonal adjustment.
  • This method has given us some challenges related to the seasonally adjusted historical series. The reason is that series older than the base year are not additive. Longer seasonally adjusted time series have been requested by many external users and the lack of additivity has led us to change the seasonal adjustment method, see below.

Changes in method

The new method for seasonal adjustment of QNA figures address:

  • Level differences between the unadjusted and seasonally adjusted data due to chaining method when a new base year is established
  • Changes in seasonal patterns when the QNA series are benchmarked against the final annual accounts and the reference year is replaced.

We apply the indirect method on the individual series and then sum the series to its respective aggregate, but the period of revision is limited from the year before the base year to the present (where the figures are additive). For the years preceding the base year we keep the figures calculated from the direct seasonal adjustment approach. This means that the seasonal adjusted time series for QNA are kept constant from 1978 to the base year.

When a new base year is established, and the time series are updated, we use identical seasonal adjustment factors as before. This means that changes in seasonally adjusted data are only due to changes in the unadjusted data.

Note that we use information from the entire period of the time series to estimate seasonal adjustment factors, but we use this information only from the year before the base year to the present.

For certain aggregates the use of the indirect and direct approach will yield different results and thus the new time series may portray a different path than previously published figures.

The method chosen is in accordance with the ESS-Guidelines on seasonal adjustment .

Special Cases

Because of the large discrepancy between the old and the new method, some series have been specially treated. This is series for gross domestic product at market and basic prices. These series are first adjusted indirectly for the whole period 1978-2008 and afterwards the seasonal factors have been normalized so that both the unadjusted and adjusted series have the same annual level.

Seasonally adjusted series

Several hundred series are seasonally adjusted every quarter. The series are adjusted at a disaggregated level and then summed up to the main aggregates.

The series for gross value added are adjusted directly, as apposed to being calculated as the difference between production and intermediate consumption.

For final consumption expenditure of households, the series are seasonally adjusted by applying the seasonal factors that are estimated for the index of household consumption of goods (see the documentation for seasonal adjustment of the index of household consumption of goods).

The following tables give an indication of the seasonal patterns for the most important macroeconomic main aggregates. The first table shows the estimated correction factors for 2014 based on prior data by direct adjustment with X-12-ARIMA. The actual factors however will not be identical since they are estimated again when new data are available. The second table shows the means of the actual seasonal factors for the period 2007-2013 as a result of indirect adjustment of many series.


The results show that the activity in the Norwegian economy systematically is highest in the 4th quarter. We also see that the activity is lowest in the 1st quarter for most of the main series except for total exports and gross domestic product where the lowest values are found in the 3rd quarter. Another important feature is that the tables show that the expected seasonal correction factors for 2014 match the actual seasonal factors in the previous years quite well. This implies that applying a direct or an indirect method for adjusting the main aggregates does not influence the results considerably. 


Pre-treatment routines/schemes

Pre-treatment is an adjustment for variations caused by calendar effects and outliers.

  • Running a detailed pre-treatment of some series/main series. The remaining series are treated by using standard options in the seasonal adjustment tools.

Comments : The series for final consumption expenditure are seasonally adjusted based on monthly series from the index of household consumption of goods.

Calendar adjustment

Calendar adjustment involves adjusting for the effects of working days/trading days and for moving holidays. Working days/trading days adjustments are made for both the number of working days/trading days and for the varying composition of days from one month to another.

  • It is performed calendar adjustments on all series showing significant and plausible calendar effects within a statistically robust approach, such as regression or RegARIMA (a regression model with an ARIMA structure for the residuals).

Methods for trading/working day adjustment

  • RegARIMA correction – in this case, the effect of trading days is estimated in a RegArima framework. The effect of trading days can be estimated by using a correction for the length of the month or leap year, regressing the series on the number of working days, etc. In this case, the residuals will have an ARIMA structure.

Correction for moving holidays

  • Automatic correction. If performed by X-12-ARIMA, automatic correction of raw data will be based on US holidays.

Comments : Except for final consumption expenditure for households where the Norwegian calendar is used.

National and EU/euro area calendars

  • Use of default calendars. The default in X-12-ARIMA is the US calendar.

Comments : Final consumption expenditure for households uses the Norwegian calendar.

Treatment of outliers

Outliers, or extreme values, are abnormal values of the series

  • Outliers are detected automatically by the seasonal adjustment tool. The outliers are removed before seasonal adjustment is carried out, and then reintroduced into the seasonally adjusted data.

Model selection

Pre-treatment requires choosing an ARIMA model, as well as deciding whether the data should be log-transformed or not.

  • Model selection is primarily automatic, but in some cases models are selected manually

Comments : Manual model selections take place when X-12-ARIMA rejects the five alternative models that are automatically tested. In these cases the so-called airlines model is chosen: (0, 0, 1)(0, 0, 1)

Decomposition scheme

The decomposition scheme specifies how the various components – basically trend-cycle, seasonal and irregular – combine to form the original series. The most frequently used decomposition schemes are the multiplicative, additive or log additive.

  • Manual decomposition scheme selection after graphical inspection of the series.

Comments : Additive decomposition is used for series with negative values, otherwise multiplicative decomposition is used.

Seasonal adjustment

Choice of seasonal adjustment approach

  • X-12-ARIMA

Consistency between raw and seasonally adjusted data

In some series, consistency between raw and seasonally adjusted series is imposed.

  • No constraints are applied.

Comments : Seasonally adjusted series in the QNA are not required to sum up to the annual raw figures. Nevertheless we choose to publish identical annual figures of unadjusted and seasonally adjusted series

Consistency between aggregate/definition of seasonally adjusted data

In some series, consistency between seasonally adjusted aggregates and its components is imposed. For some series there is also a special relationship between the different series, e.g. GDP which equals production minus intermediate consumption.

  • Definitions and relationships that hold for unadjusted figures also apply for seasonally adjusted figures.

Comments : The supply side equals the use side also for seasonally adjusted figures. This implies that changes in stocks/statistical discrepancies are treated as a residual in the seasonally adjusted figures (balancing item). The series for gross value added are adjusted directly (see chapter 1.3) and are not required to match the difference between seasonally adjusted series for production and intermediate consumption (thus, vertical – not horizontal – consistency is imposed).

Direct versus indirect approach

Direct seasonal adjustment is performed if all time series, including aggregates, are seasonally adjusted on an individual basis. Indirect seasonal adjustment is performed if the seasonally adjusted estimate for a time series is derived by combining the estimates for two or more directly adjusted series.

  • Mixed indirect approach where the seasonal adjustment of components possibly occur using different approaches and software.

Comments : QNA uses aggregation routines outside X-12-ARIMA.

Horizon for estimating the model and the correction factors

When performing seasonal adjustment of a time series, it is possible to choose the period to be used in estimating the model and the correction factors. Correction factors are the factors used in the pre-treatment and seasonal adjustment of the series.

  • The whole time series is used to estimate the model and the correction factors
  • The whole time series is used to estimate the correction factors. Only part of the time series is used to estimate the model.

Comments : For most series the whole time series is used for estimating the model and correction factors, but for some series only part of the time series is used to estimate the model.

Audit procedures

General revision policy

Seasonally adjusted data may change due to a revision of the unadjusted (raw) data or the addition of new data. Such changes are called revisions, and there are several ways to deal with the problem of revisions when publishing the seasonally adjusted statistics.

  • Seasonally adjusted data are revised in accordance with a well-defined and publicly available revision policy and release calendar.

The following table gives an indication of the expected growth rate revisions from the previous period when we compare the initial and final published data. This only applies to revisions caused by seasonal adjustment routines where revisions of raw data are not considered.

The figures for gross domestic product for Mainland Norway show that the seasonally adjusted growth rate from the previous period is exposed to a revision of 0.2 percentage points when new observations are added. It turns out that figures for the 1st quarter are subject to the least revisions. The table shows that gross fixed capital formation, exports and imports are most likely to be revised.


Concurrent versus current adjustment

  • The model, filters, outliers and regression parameters are re-identified and re-estimated continuously as new or revised data become available.

Horizon for published revisions

  • The individual series will be revised when seasonal factors are re-estimated. Concerning the main aggregates the period of revisions is limited from the base year to the present. This means that seasonally adjusted data for quarterly national accounts are held constant from 1978 to the base year.

Comments : This applies as long as the unadjusted figures before the base year remains unchanged. When a new base year is established, and the time series are updated, we use identical seasonal adjustment factors as before. This means that changes in seasonally adjusted data are only due to changes in the unadjusted data.

Quality of seasonal adjustment

Evaluation of seasonally adjustment data

  • Continuous/periodical evaluation using standard measures proposed by different seasonal adjustment tools.

Quality measures for seasonal adjustment

  • For most of the series, a selected set of diagnostics and graphical facilities for bulk treatment of data is used.

Table of quality measurement for this statistics:

For more information on the quality indicators in the table please refer to: metadata on methods: seasonal adjustment .

Comments to the table of qualitative indicators

All series were adjusted with the multiplicative method. The results of main aggregates’ are calculated via a direct adjustment with X-12-ARIMA. Although these series in practice are indirectly adjusted, we may claim that the results are still valid (see chapter 1.3)

X-12-ARIMA chooses automatically the most appropriate model for the individual series, apart from the series for gross fixed capital formation in extraction and transport via pipelines , gross domestic product for Mainland Norway, gross value added for production of other goods and gross value added for service activities, where the model is chosen manually.

Most aggregates do not show any trading day effects. Nevertheless, the location of the Easter holidays are significant for half part of the aggregates.

ANOVA shows that the rates of change for the original series are primarily due to seasonal effects. The contribution from trend and the irregular component is particularly relevant for final consumption expenditure of general government, gross fixed capital formation in extraction and transport via pipelines and exports. For GDP almost 87 per cent of the change in the raw data is explained by season. The rest is mostly explained by trading days and trend.

ASA and ACH were calculated for the period 2011-2013. The results show that revisions of the growth rates from the previous quarter ranged from 0.2 percentage points for GDP to 1.4 percentage points for export crude oil and natural gas .

M- and Q-values for the main aggregates indicate that some of the series (household final consumption expenditure, final domestic use of goods and services and GDP) are adjusted with satisfactory results. Nevertheless both levels and rates of change for the latest periods are exposed to revisions. The series may have some irregular fluctuations.

The remaining series are adjusted with questionable results. Levels and rates of change may have a great deal of variation in the most recent figures. The results should be interpreted with caution.

Special cases

Seasonal adjustment of short time series

  • All series are sufficiently long to perform an optimal seasonal adjustment.

Treatment of problematic series

  • For some series only recent years of the series are used to seasonally adjust the series, because deleting earlier data makes it possible to find a model/adjustment of reasonable quality.

Comments : Some problematic series are aggregated before they are seasonally adjusted. An example of such a series is gross value added for refined petroleum products which fluctuates between positive and negative levels. In order to avoid influencing GDP in an inappropriate way, this series is put together with gross value added for other chemical products, and the sum of the two industries are seasonally adjusted.

Posting procedures

Data availability

  • Both unadjusted (raw) and seasonally adjusted data are available.

Comments : However, not all seasonally adjusted figures are published.

Press releases

  • In addition to raw data, at least one of the following series is released: pre-treated, seasonally adjusted, seasonally plus working day adjusted trend-cycle series.
  • Both levels and growth rates are presented.
  • Empirical values are presented to evaluate revisions of data in earlier press releases.