On seasonal adjustment of sickness absence, self-certified and doctor-certified

1. WHAT IS SEASONAL ADJUSTMENT?

2. PRE-TREATMENT

3. SEASONAL ADJUSTMENT

4. REVISIONS POLICIES

5. QUALITY OF SEASONAL ADJUSTMENT

6. SPECIFIC ISSUES ON SEASONAL ADJUSTMENT

7. DATA PRESENTATION ISSUES

8. REFERENCES:

1. WHAT IS SEASONAL ADJUSTMENT?

1.1 What is seasonal adjustment?

Monthly and quarterly time series are often characterised 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: metadata on methods: seasonal adjustment

1.2 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 (1^st and 4^th quarter) partly due to respiratory infections.

Scheduled (vacation corrected) man-days in the quarter also shows a clear seasonal pattern, with fewer man-days in the summer half year, especially 3^rd quarter due to summer holidays.

Both scheduled (vacation corrected) 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.

1.3 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 (vacation corrected) 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.

2. PRE-TREATMENT

2.1 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:

1. 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 pre-adjusted with the same influenza variable based on sickness absence man-days certified by a doctor although it is not a direct link. Stil the variable has a very significant effect.

2. Scheduled man-days are vacation corrected based on proportions of absence on holiday from LFS (see About the Statistics item 4.1). The vacation correction from LFS introduce a seasonal effect, variation Easter in March, and a positive trend (see StatBank table 04545) in this denominator before we start the seasonal adjustment. Due to the trend in the proportions of absence on holiday, we pre-adjusted scheduled man-days with a gender divided proportions of absence on holiday from the LFS that are differentiated and deseasonalized.

2.2 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.

2.2.1 Methods for trading/working day adjustment

• No correction.

Comments:

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

2.2.2 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, 2^nd 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 less good results according to our AICC tets.

2.2.3 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.

2.3 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 are not done between the annual reviews.

So far only two cases of Outliers are predefined and incorporated:

Ø Level shift in the sickness absence man-days certified by a doctor between 2^nd and 3^rd quarter 2004 (doctor certification reform)

Ø Additive outlier 3^rd quarter 2009 for self-certified sickness absence man-days¹ (beginning of the swine influenza )

2.4 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:

Automdl{}-procedure i version 0.3 of X-12-ARIMA is applied with standard options².

2.5 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.

3. SEASONAL ADJUSTMENT

3.1 Choice of seasonal adjustment approach

• X-12-ARIMA

3.2 Consistency between raw and seasonally adjusted data

• Do not apply any constraint.

3.3 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, see item 3.4.

3.4 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

Ø doctor-certified sickness absence man-days

Ø self-certified sickness absence man-days

Ø 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.

3.5 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

4. REVISION POLICIES

4.1 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.

4.2 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.

4.3 Horizon for published revisions

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

5. QUALITY OF SEASONAL ADJUSTMENT

5.1 Evaluation of seasonally adjustment data

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

5.2 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:

http://www.ssb.no/a/english/kortnavn/sykefratot_en/kvalitetsindikatorer-en.xls

For more information on the quality indicator in the table see:
metadata on methods: seasonal adjustment

6. SPECIFIC ISSUES ON SEASONAL ADJUSTMENT

6.1 Seasonal adjustment of short time series

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

6.2 Treatment of problematic series

• All problematic series are treated in a special way.

Comments:

Sickness absence man-days

Influenza irregularities are a special challenge in the seasonal adjustment of this statistics. 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 (See item 2.1).

Scheduled (vacation corrected) man-days

Scheduled man-days are vacation corrected based on proportions of absence on holiday from LFS (see About the Statistics item 4.1). The vacation corrections from LFS introduce a seasonal effect, variation Easter in March, and a small positive trend (see StatBank table 04545) in scheduled man-days (denominator) before we start the seasonal adjustment. Due to the trend in the proportions of absence on holiday, we pre-adjusted scheduled man-days with gender divided proportions of absence on holiday (LFS) that are differentiated and deseasonalized. The differentiation removes much of the trend in the pre-adjustment variable.

7.1 Data availability

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

Comments:

Both seasonally adjusted data and seasonal and influenza adjusted data are available.

7.2 Press releases

Options:

• 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 (attachment to this document, see item 5.2).

8. REFERENCES:

Statistics Norway’s metadata on methods: seasonal adjustment

EUROSTAT: Seasonal Adjustment. Methods and Practices

US census: X-12-ARIMA-manual

Dinh Quang Pham: Time series and basic seasonal adjustments and X-12-ARIMA, Reports 2001/2, Statistics Norway

ESS-Guidelines X-12-ARIMA-manual Seasonal Adjustment. Methods and Practices

¹ 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.

² The Pickmdl{}-procedure in X-12-ARIMA do not manage to select a ARIMA model in a satisfactory way for all the series for self-certified sickness absence man-days. The procedure gives a warning about evidence of seasonal overdifferencing, and suggests setting the model manually.