Retail sales, investment statisticsQ4 2013


About seasonal adjustment

General information on seasonal adjustment

Monthly and quarterly time series are often characterised by considerable seasonal variations, which can 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 using 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?

Historical data for investments for the retail sales industry (DETINV) reveal a clear pattern of higher investments towards the end of the year, i.e. in the 4th quarter. There could be many reasons for this, such as if a company decides to use up its entire investment budget before the end of the current year, or if they are registering the investments at the end of the year, etc. These patterns can complicate the interpretation of the time series from quarter to quarter. In order to enable an analysis of the underlying development of the investments of the retail sales industry, the timeseries are adjusted for seasonality.

Seasonally adjusted series

The investment for the retail sales industry are made up of four timeseries; retail trade, except of motor vehicles, motorcycles and automotive fuel, machines and Inventory, motor vehicles and other means of transport, and new buildings and renovation. All four timeseries are seasonally adjusted using the same model and method.


Pre-treatment routines/schemes

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

No pre-treatment is performed on the timeseries.Checks are carried out for outliers.

Calendar adjustment

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

No correction.

Methods for trading/working day adjustment

No correction.

Correction for moving holidays

Correction based on an estimation of the duration of the moving holidays effects, specifically adjusted to Norwegian circumstances.

No correction.

National and EU/euro area calendars

Use of the Norwegian calendar

Treatment of outliers

Outliers, or extreme values, are abnormal values in the series.

The software automatically detects additive outliers, and temporary- and lasting level shifts.

Model selection

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

Manual selection of model after statistical tests have been carried out. 

Comments :
Following statistical tests, the ARIMA model (0,1,1) (0,1,1) has been chosen, where the time series have been log-transformed.

 Decomposition scheme

The decomposition scheme specifies how the various components – 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

X-12-ARIMA Version 0.3

Consistency between raw and seasonally adjusted data

No consistency conditions imposed.

Consistency between aggregate/definition of seasonally adjusted data

No consistency conditions 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.

A direct approach is used where the seasonal adjustment of components occurs using the same approach and software for each individual timeseries.

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 for 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 can 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 seasonally adjusted statistics.

The seasonally adjusted- and trendseries will change when a new time period (quarter) is added to the time series.

Concurrent versus current adjustment

The model, filters and calendar regressors are re-identified once a year and the respective parameters and factors are remain fixed between the yearly reviews.

Comments :
The seasonality filter for retail trade, except of motor vehicles, motorcycles and automotive fuel, and new buildings and renovation is 3x5. For machines and inventory, and motor vehicles and other means of transport the seasonality filter is 3x9. The trendfiler for all four timeseries is 3x5.

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 adjusted 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.

The quality measures for the four timeseries in DETINV vary. The series for retail trade, except of motor vehicles, motorcycles and automotive fuel, and machines and Inventory have good quality measures. The series for motor vehicles and other means of transport, and new buildings and renovation have poor quality measures. The poor level of the quality measures for motor vehicles and other means of transport means that adjusting for seasonality is not normally recommended.

In order to keep the seasonal adjustment to remain consistent, seasonal adjustment will be used on all four timeseries.

Special cases

Seasonal adjustment of short time series

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

Treatment of problematic series

Not relevant.

Posting procedures

Data availability

Raw data-, seasonally adjusted- and trendseries are available for all four time series.