About seasonal adjustment
General information on seasonal adjustment
Montly 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
Why seasonally adjust these statistics?
Due to our shopping habits The Index of wholesale and retail trade will vary from month to month. For instance the month of December shows higher sale than the rest of the months. This combined with the influence of how the Easter holiday varies between March and April and also the influence of movable public holidays make a comparison from one month to the next difficult. To adjust for these circumstances the Index of wholesale and retail trade is adjusted for seasonal variations, so the underlying development of the index can be analyzed.
Seasonally adjusted series
The Index of wholesale and retail trade is published at the three-digit NACE level, and constitutes 10 seasonally adjusted series. There is only for the sector 47 Retail trade (except of motor vehicles and motorcycles) there is seasonally adjusted series. There will be seasonally adjusted series also for the sector 45 Wholesale and retail trade and repair of motor vehicles and motorcycles and sector 46 Wholesale (except of motor vehicles and motorcycles) at a later time, when there is enough data to also seasonally adjust these series.
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.
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
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.
For 1 January , 1 May and 17 May the correction of working days has been modified so that these days are regarded as a Sunday.
Correction for moving holidays
Correction based on an estimation of the duration of the moving holidays effects, specifically adjusted to Norwegian circumstances.
National and EU/euro area calendars
A calendar based on Norwegian holidays is used.
Treatment of outliers
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.
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.
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.
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.
Do not apply any constraint.
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.
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
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.
Both raw and seasonally adjusted data are revised between two consecutive official releases of the release calendar.
Raw data is not revised.
Concurrent versus current adjustment
Partial concurrent adjustment: the model is identified and estimated yearly, while filters, outliers and regression parameters are re-identified and estimated continuously as new or revised data become available.
Factors concerning the Easter holyday are estimated yearly.
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
Evaluation of quality based only on graphical inspection and descriptive statistics.
A model where the various quality indicators will be evaluated continuous/periodically in the future.
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.
Seasonal adjustment of short time series
All series are sufficiently long to perform an optimal seasonal adjustment.
Treatment of problematic series
None of the published series are viewed as problematic.
Raw data, pre-treated data and seasonally adjusted series are available.
All metadata information associated with an individual time series is available.
In addition to raw data, at least one of the following series is released: Seasonally plus working day adjusted.
- Notat 2009/27 Dokumentasjon av sesongjustering i SSB
- ESS-Guidelines on seasonal adjustment
- US census: X-12-ARIMA-manual
- Nye US Census-baserte metoder for ukedageffekter for norske data
- Notat 2007/43 Ny metode for påskekorrigering for norske data
- Notat 2001/54 Sesongjustering av tidsserier, Spektralanalyse og filtrering
- Notat 2001/02 Innføring i tidsserier, Sesongjustering og X-12-ARIMA