Index of household consumption of goodsNovember 2014


About seasonal adjustment

General information on 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 adjustir="ltr" align="lement in order to remove the effects of these seasonal fluctuations. Once data have been adjusted for seasonal effects by X-13-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?

The index of household consumption of goods is an indicator which in addition to retail sales, takes into consideration purchases of cars and motorbikes. The households’ consumption of electricity and heating fuels is also included in the index. The purchases/consumption are affected by for instance the number of days in a month where one can register a car and shop, the temperatures and holidays – so-called seasonal and calendar effects. To ease the comparability with previous periods, the figures are seasonally adjusted.

The following table shows the aggregated series as being published and the underlying components (i.e. individual series) that are used to estimate these. The table also shows the components’ weights. These are based on the results for 2014 from the Quarterly National Accounts (QNA).

Main aggregates Codes Weights in 2014
Food, beverages and tobacco A1, A2, B1, B2 32.8
Electricity and heating fuels D4, D5 6.6
Purchases of vehicles and petrol G1, G2, G3 19.1
Other goods Remaining codes 41.4
Household consumption of all goods All 100.0
Food A1 21.6
Non-alcoholic beverages A2 3.0
Alcoholic beverages B1 4.6
Tobacco B2 3.6
Clothing and footwear C1 10.3
Materials for the maintenance and repair of dwellings D2 0.1
Electricity D4 5.6
Fuels and heat energy D5 1.0
Furnishings and household equipment E1 6.5
Miscellaneous household goods E2 4.5
Cleaning products and other articles E4 1.2
Medical products, appliances and equipment F1 1.7
Glasses and orthopedics products F2 1.0
Purchase of vehicles G1 12.2
Spare parts and accessories for personal transport equipment  G2 1.0
Fuels and lubricants for personal transport equipment  G3 6.0
Telephone and telefax equipment H2 0.8
Audio-visual, photographic and information processing equipment I1 3.1
Recreational equipment I2 2.9
Major durables for recreation and culture I4 1.3
Books and other recreational items I5 4.2
Personal goods, durable L2 0.7
Cosmetics and toaltettartikler L3 2.7
Personal effects n.e.c. L4 0.4
Household consumption of all goods All 100.0

The calculation of both unadjusted and seasonally adjusted figures for the main aggregates is based on the components. Almost all of these components have a clear seasonal pattern. In section 1.3 the characteristics of some of the series are commented on. Turnover from retail sales, which represent approximately 80 per cent of the main index, is the main source when estimating the different series. The following factors affect the monthly turnover/consumption regardless of the underlying evolution:

  • Number of days in a month. Given identical conditions, the turnover in February is lower than in January, which is valid for all series.
  • Number of different days of the week within the month. The number of Saturdays (high turnover) and Sundays (low turnover) is of particular interest.
  • Number of holidays within the month with particular focus on whether Ester falls in March or April.
  • Christmas shopping which systematically causes high turnover in December and low turnover in January.

For electricity it is mainly the temperatures which affect the monthly consumption. For vehicles and petrol, the high season for purchasing these goods are the summer months. If one wishes to compare two different periods having different seasonal patterns, it is important to identify the size of the seasonal effects. This is the reason for seasonally adjusting the index of household consumption of goods.

Seasonally adjusted series

We have chosen to first adjust all individual components and thereafter aggregate them to calculate the main aggregates. This means that the connection between the aggregates is also valid for seasonally adjusted figures. By adjusting indirectly, we obtain at least as good results as if we had adjusted the main aggregates directly.

To arrive at this conclusion, one has to use the table in chapter 5. That table shows the quality of the seasonally adjusted figures as well as other analyses in the form of diagrams and figures from X-13-ARIMA.

Even though the seasonal pattern for the individual series can change over time, we can still draw some conclusions regarding the main aggregates. The graphs below show the expected correction factors for 2015 using the same assumptions as documented in the following chapters.

Expected correction factors 2015


The series for the household consumption of all goods (i.e. the main index) shows that the highest turnover is in December and the lowest in January and February (Christmas effects). For the period May – November seasons are less relevant. How March and April are treated, depends on when Easter falls. If Easter falls in April, there will be only minor corrections as it will be considered as part of the normal season. The adjustments will be larger if Easter falls in March.

As regards seasonal adjustment of electricity consumption, the graph shows that this series has a very clear and strongly defined seasonal pattern, shaped as a U, within the year. The main reason is the temperatures. In April and October, there are hardly any adjustments as it is considered as average annual consumption. January and December are the two months that are adjusted most (approximately 30 per cent). The consumption is lower in February than in March, which is due to there being fewer days in February.

Lastly we see that May, June and especially July are the months with the highest turnover for vehicles and petrol. The turnover for this series is clearly lower in January and February than all other months in the year.


Pre-treatment routines/schemes

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

  • 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.

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.

  • 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).

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.

Correction for moving holidays

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

Comments : Easter and Whitsun are corrected for if being significant.

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 : In the index of household consumption of goods the Norwegian calendar is in use.

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.

  • Automatic model selection by established routines 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.

  • Automatic decomposition scheme selection.

Comments : In the index of household consumption of goods log additive decomposition is in use.

Seasonal adjustment

Choice of seasonal adjustment approach

  • X-13-ARIMA

Consistency between raw and seasonally adjusted data

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

  • In the index of household consumption of goods, the equality over the year of seasonally adjusted data to the unadjusted data (e.g. sum or average) is imposed.

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.

Comments : In the index of household consumption of goods this is not relevant.

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.

  • We use 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 are used to estimate the model and the correction factors.
  • Only part of the time series is used to estimate the correction factors and the model.

Comments : The series start in 2000 to estimate the model and the correction factors.

Audit procedures

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.

Comments : Due to Statistics Norway giving high priority to timeliness, the index of household consumption of goods may have to rely on preliminary estimates in some cases. This means that such estimates will be replaced in subsequent releases. As regards the seasonally adjusted figures, the figures for previous periods may be revised when a new observation is added to the series of raw data. Revised figures are published in the official monthly release of the index of household consumption.

In the following table , indications are given regarding expected revisions for seasonally adjusted rates of change for the main aggregates when adjusted directly.

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

  • The last 4 years  in  time series are  revised in the event of a re-estimation of  the seasonal factors. History before T-4  keeps unchanged  provided no changes in the unadjusted data.

Quality of seasonal adjustment

Evaluation of seasonally adjustment data

  • Continuous 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 following table is a table of quality measurement for this statistics. For more information on the quality indicators in the table see: metadata on methods: seasonal adjustment.

Comments to the table of qualitative indicators
All series are adjusted with the multiplicative method. The main aggregates’ results are calculated via X-13-ARIMA even though these series in practice are adjusted indirectly.

X-13-ARIMA chooses automatically the most appropriate model for the individual series, except for major durables for recreation and materials for the maintenance and repair of dwellings where the model is chosen manually.

ANOVA shows that the rates of change for the original series are primarily due to seasonal and trading day effects and not due to the trend. The contribution from the irregular component is also low. We see for the total index, that more than 99 per cent of the rate of change value is due to seasonal and trading day effects.

ASA and ACH are calculated for 2012-2014. The results for the main aggregates show that revisions of the rates of changes from the previous month  ranged from 0,4 percentage points for food, beverages and tobacco to 1,3  percentage points fo spare parts and accessories for personal transport equipment . For the total household consumption of goods, the expected revision of the seasonally adjusted rates of change was approximately 0.3 percentage points.

M and Q values for the main aggregates indicate that the series are well adjusted. The levels and rates of change for the most relevant figures are rarely subject to revision. The seasonal pattern is clearly identified and removed. Both the seasonal pattern and the irregular component are stable.

Special cases


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.


Posting procedures

Data availability

  • Raw and seasonally adjusted data are available.
  • All metadata information associated with an individual time series is available.

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 and/or trend-cycle series.
  • Only levels or different forms of growth rates are presented.
  • For each series, some quality measures of the seasonal adjustment are presented.

Comments : In addition to the raw data, seasonally adjusted series are published both as an index and as growth rates (change in per cent compared with the previous month). The seasonally adjusted index and the trend are published graphically in the Monthly Bulletin of Statistics.


Statistics Norway’s metadata on methods: seasonal adjustment

The Committee for Monetary, Financial and Balance of Payments statistics: ESS-Guidelines on seasonal adjustment

EUROSTAT: Seasonal Adjustment. Methods and Practices  

US census: X-13-ARIMA-manual.

Dinh Quang Pham: Nye US Census-baserte metoder for ukedagseffekter for norske data, Notater 2008/58, Statistisk sentralbyrå