National accountsNovember 2020


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 months or 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 MNA which has to be given specific attention compared to other short time economic indicators:

·        The series for the main aggregates in the MNA is a result of aggregation of many components. 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.

·        Data may be exposed to some revisions each month as well as major revisions when the the preliminary national accounts are reconciled with final national accounts

Background information

·        To seasonally adjust the GDP (and all other aggregates) we use 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. 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.

·          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.

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

Seasonally adjusted series

Over a thousand series are seasonally adjusted every month. The series are adjusted at a disaggregated level and then summed up to the main aggregates.

The series for gross value added at industry level are adjusted directly, as opposed 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).



Pre-treatment routines/schemes

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

  • We run a pre-treatment of some series/main series.

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

  • We run an automati correction with X-12-ARIMA. The utomatic correction of raw data will be based on Norwegian holidays.

National and EU/euro area calendars

  • Use of the Norwegian calendar with X-12-ARIMA.

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.

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 and additive.

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

Comments : Additive decomposition is used for series with (potential) negative values or values equal zero, 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.


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 is applied

Comments : MNA 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


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 numbers are revised in accordance with a well-defined and publicly available revision policy and release calendar.


Concurrent versus current adjustment

  • The model, filters, outliers and regression parameters are re-identified and re-estimated 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.

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.


Special cases

All series are sufficiently long to perform a seasonal adjustment.


Posting procedures

Data availability

  • Both unadjusted (raw), seasonally adjusted and sum rolling three months data are available.

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.