Sickness absenceQ1 2017


About 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-13ARIMA-SEATS or some other seasonal adjustment tool, a clearer picture of the time series emerges.

For more information on seasonal adjustment: metadata on methods: seasonal adjustment.

Why seasonally adjust these statistics?

Why do we seasonally adjust sickness absence, self-certified and doctor-certified?

The quarterly statistics of self-certified and doctor-certified sickness absence shows a clear seasonal pattern. Sickness absence man-days for employees self-certified and certified by a doctor are a lot higher in the winter half year (1st and 4th quarter) partly due to respiratory infections.

Both scheduled and lost man-days are influenced by the number of working-days in the quarter, which is defined as weekdays (Monday – Friday) in the quarter deducted by holidays and public days off on weekdays in the quarter.

Seasonally adjusted series

The following quarterly time series are seasonally adjusted separately for men and women:

  • Sickness absence man-days certified by doctor
  • Self-certified sickness absence man-days
  • Scheduled man-days

Primarily we publish sickness absence rates, which are sickness absence man-days in per cent of scheduled man-days. We publish sickness absence rates, by type of certification (self-certified, certified by doctor) and gender.



Pre-treatment routines/schemes

Running a detailed pre-treatment. This means using models which are specially adapted for the pre-treatment of the raw data for a given series.

Comments :

The sickness absence man-days variables are pre-adjusted with a deseasonalized variable for the proportion of sickness absence man-days certified by a doctor with influenza diagnosis, by gender. Also, self-certified sickness absence man-days are pre-adjusted with the same influenza variable based on sickness absence man-days certified by a doctor although it is not a direct link. Still, the variable has a very significant effect.


Calendar adjustment

To perform 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). The regression variables for the calendar adjustment are adapted to reflect the working days, public holidays and so forth specific to Norway.

Methods for trading/working day adjustment

No correction.

Comments : Trading day variables (based on Norwegian calendar) are not significant for these quarterly time series.


Correction for moving holidays

No correction.

Comments : All the variables are pre-adjusted with the number of working days in the quarter, deseasonalized. The number of working days in the quarter is defined as the number of weekdays (Monday – Friday) in the quarter subtracted by the number of Norwegian common days off that falls on weekdays. The moving holidays Maundy Thursday, Good Friday, 2nd Easter day, Whit Monday and Ascension Day are here included. A separate Easter variable is not included, because it doesn’t have a significant effect when the number of working days variable is included, and pre-adjusting with an Easter variable instead of the number of working days variable gives worse results according to our AICC tests.


National and EU/euro area calendars

Use of the Norwegian calendar or the EU/euro area calendar as appropriate; the EU/euro area calendar is based on the mean number of working days in the different member states.

Comments : All the variables are pre-adjusted with the number of working days in the quarter, deseasonalized. The number of working days in the quarter is defined as the number of weekdays (Monday – Friday) in the quarter subtracted by the number of Norwegian common days off that falls on weekdays. Other than the moving holidays, this includes our red-letter days: New Year's Day, International Workers' Day (May 1 st ), Constitution Day (May 17 th ), Christmas Day, Boxing Day and that may fall on weekdays.


Treatment of outliers

The series are checked for outliers of different types. Once identified, outliers are explained/modelled using all available information. Outliers for which a clear interpretation exists (strikes, consequences of (government) policy changes etc.) are included as regressors in the model.

Comments : Outliers are detected automatically (of all types) in the annual review or in case of special need. Continuous automatic detection of outliers is not done between the annual reviews.

So far only a few of outliers are predefined and incorporated:

  • Level shift in the sickness absence man-days certified by a doctor between 2 nd and 3 rd quarter 2004 (doctor certification reform)
  • Additive outlier 3 rd quarter 2009 for self-certified sickness absence man-days for men (beginning of the swine influenza). (Also, self-certified sickness absence man-days pre-adjusted with the proportion of doctor-certified sickness absence man-days with influenza diagnosis, by gender (deseasonalized) although it is not a direct link. The pre-adjustment variable adjusts the effect of influenza irregularities well except in the beginning of the Swine influenza, when the predefined outlier variable is defined.)
  • Due to transition to the A-Scheme register between 2014 and 2015, a level shift (LS2015.1) is specified for all time series. (The risk of the quality of the seasonally adjusted figures is greater for unspecified break than for specified "non-break", which lead to parameter estimates close to zero and loss of a degree of freedom. That is the reason for the specification of the non-significant level shift 2015K1 for doctor-certified sickness absence for women. (For a discussion, please see chapter 7 in Handbook on Seasonal Adjustment 2018 edition, Eurostat)
  • Seasonal outlier (SO2015.1) is also specified for contractual man-days, due to transition to the A-Scheme register


The focus of the dissemination of sickness absence statistics is on the seasonal, calendar and influenza adjusted sickness absence. In addition, these time series are also adjusted for the break in the time series due to the A Scheme register from 2015. Statistics Norway believes that these figures give the best picture of the underlying development in sickness absence from quarter to quarter. For those who want numbers that are only seasonally adjusted, these are also published in StatBank.

Model selection

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

Automatic model selection by established routines in the seasonal adjustment tool.

Comments : The automdl{}-procedure in X-13ARIMA-SEEATS is applied for selecting the best ARIMA model in the annual reviews, with the following options (recommended in the US Census Bureau Guideline):

automdl{ mixed=no   balanced=yes  maxdiff=(1 1)  maxorder=(2 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.

Automatic decomposition scheme selection.

Seasonal adjustment

Choice of seasonal adjustment approach



Consistency between raw and seasonally adjusted data

Do not apply any constraint.


Consistency between aggregate/definition of seasonally adjusted data

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

Impose the equality between aggregated series and the component series.


Comments: The equality result from the indirect method.


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.

Indirect approach where the seasonal adjustment of components occurs using the same approach and software, and then totals are derived by aggregation of the seasonally adjusted components.

Comments: The following time series are seasonally adjusted separately for male and female:

  • doctor-certified sickness absence man-days
  • self-certified sickness absence man-days
  • scheduled man-days (in the quarter)

The seasonally adjusted figures for male and female together results from adding seasonally adjusted figures for male and for female.


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

Concurrent versus current adjustment

Partial concurrent adjustment: The model, including possible log transformation, lengths of filters, outliers and calendar regressors are identified once a year, and the respective parameters and factors re-estimated every time a new or revised data becomes available.

Horizon for published revisions

The entire time series is revised in the event of a re-estimation of the seasonal factors.

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 see:  metadata on methods: seasonal adjustment

Special cases

Seasonal adjustment of short time series

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

Treatment of problematic series

All problematic series are treated in a special way.

Influenza irregularities are a special challenge in the seasonal adjustment of sickness absence man-days. Sickness absences due to influenza are normally high in 1 st quarter, sometimes high in 4 th quarter and sometimes low in the winter half-year. Without pre-adjusting for irregular influenza, the uncertainty of calendar effects will increase, and the calculation of seasonal component may be more unstable. The sickness absence man-days variables are therefore pre-adjusted with a deseasonalized variable for the proportion of sickness absence man-days certified by a doctor with influenza diagnosis.

Following the Corona crisis that started in the 1st quarter of 2020, the seasonal adjustment of sickness absence follows the Eurostat guidelines for how to treat this extraordinary event. The result being that the effect of the Corona crisis is not a part of the foundation of the seasonal patterns, since the period has been modelled as an outlier or extreme value in all the series. Furthermore, we have extended our adjustment of influenza irregularities to also include sickness absence due to the Corona virus. Since we do not have perfect information about how Corona-related symptoms have been diagnosed, it is advisable to interpret these with some caution.

Posting procedures

Data availability

  • Raw and seasonally adjusted data are available.
  • Historical data are available to enable revision analysis.

Comments: Both seasonally adjusted data and seasonal, calendar, influenza and A-Sheme break adjusted data are available in our StatBank.

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.

For each series, some quality measures of the seasonal adjustment are presented.