Consumer price indexDecember 2015


About seasonal adjustment

General information on seasonal adjustment

General information on seasonal adjustment

Monthly and quarterly time series are often characterized by considerable seasonal variations, which might complicate their interpretation. Such time series are therefore subjected to a process of seasonal adjustment in order to remove the effects of these 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 emerges.

For more information on seasonal adjustment: Documentation of seasonal adjustment in Statistics Norway.

Why seasonally adjust these statistics?

The Consumer Price Index (CPI) is an indicator build up of many different sub aggregates. Some of these sub aggregates show a clear seasonal pattern, for instance the price index of clothing and footwear where seasonal sales are common. To make the comparability with earlier periods easier, the figures are seasonally adjusted.

A seasonally adjusted CPI can be interpreted as one of many indicators trying to identify the underlying inflation in the original series.

Seasonally adjusted series

Seasonally adjusted series are only published for the CPI all-item index and the all-item index of CPI adjusted for tax changes and excluding energy products, CPI-ATE.

An indication of the seasonal pattern for the two all-item indices are shown below. The first table shows expected estimated correction factors for 2017 based on earlier data with the help of direct adjustment by X-12-ARIMA. Actual factors are not identified since these must be estimated when new data is available. The second table shows actual average of the seasonal adjustment factors for the period 2012-2016. Link to tables .

The tables show that the expected factors for 2017 are close to the average seasonal factors indicating a stabile seasonal pattern. The factors in the table are close to 100 indicating a low level of adjustment of the original series.


Pre-treatment routines/schemes

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

There are no pre-treatment of raw data.

Calendar adjustment

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

Not relevant for the CPI series.

Methods for trading/working day adjustment

Not relevant for the CPI series.

Correction for moving holidays

Not relevant for the CPI series.

National and EU/euro area calendars

Not relevant for the CPI series.

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 automatic using established procedures in the seasonal adjustment tool.

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.

Multiplicative method is in use.

Seasonal adjustment

Choice of seasonal adjustment approach


Consistency between raw and seasonally adjusted data

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

Do not apply any constraint.

Consistency between aggregate/definition of seasonally adjusted data

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

Not relevant for the CPI series, no adjustment of the aggregates.

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.

Direct approach is used.

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.

For the CPI and the CPI-ATE the time series from 1985 and 1995 respectively, are used.

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 each time it is published.

Comments : There is no revision in original series. For the seasonally adjusted series, new data can lead to revision in the seasonally adjusted series.

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

Both the CPI and the CPI-ATE are revised back to 2012; before 2012 the seasonal adjusted figures are final.

Quality of seasonal adjustment

Evaluation of seasonally adjustment data

Periodical evaluation using standard measures proposed by different seasonal adjustment tools.

Quality measures for seasonal adjustment

Additional specific tests are computed to complement the set of available diagnostics within the seasonal adjustment tool.

A table containing selected quality indicators for the seasonal adjustment is available here; Indicators of quality in seasonal adjusted figures.

For more information on the quality indicators in the table go to: Seasonal adjustment: General information.


Special cases

Seasonal adjustment of short time series

Both series are sufficiently long to perform an optimal seasonal adjustment.

Treatment of problematic series

None of the series are considered problematic.

Posting procedures

Data availability

Unadjusted data and seasonally adjusted data are available.

Press releases

Index series are published in the StatBank.

Did you find what you were looking for?

You have turned off Javascript. You can send us your feedback at

E-mail SSB