On seasonal adjustment of the retail sales index

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 the retail sales index

Due to our shopping habits the retail sales index 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 retail sales index is adjusted for seasonal variations, so the underlying development of the index can be analyzed.

1.3 Seasonally adjusted series

The retail sales index is published in a three-digit NACE level, and constitutes 10 seasonally adjusted series.

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.

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

• 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.

Comments:

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.

2.2.2 Correction for moving holidays

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

2.2.3 National and EU/euro area calendars

• A calendar based on Norwegian holidays is used.

2.3 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.

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.

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.

• Manual decomposition scheme selection after graphical inspection of the series.

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.

• Do not apply any constraint.

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.

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.

• Both raw and seasonally adjusted data are revised between two consecutive official releases of the release calendar.

Comments:

Raw data is not revised.

4.2 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.

Comments:

Factors concerning the Easter holyday are estimated yearly.

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

• Evaluation of quality based only on graphical inspection and descriptive statistics.

Comments:

A model where the various quality indicators will be evaluated continuous/periodically in the future.

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.

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

• None of the published series are viewed as problematic.

7. DATA PRESENTATION ISSUES

7.1 Data availability

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

7.2 Press releases

• In addition to raw data, at least one of the following series is released: Seasonally plus working day adjusted.

8. REFERENCES:

SSBs Metadata - Statistiske metoder - Sesongjustering

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

EUROSTAT: Seasonal Adjustment. Methods and Practices

US census: X-12-ARIMA-manual

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

Dinh Quang Pham: Ny metode for påskekorrigering for norske data, Notater 2007/43, Statistisk sentralbyrå.

Ole Klungsøyr: Sesongjustering av tidsserier. Spektralanalyse og filtrering, Notat 2001/54, Statistisk sentralbyrå

Dinh Quang Pham: Innføring i tidsserier - sesongjustering og X-12-ARIMA, Notater 2001/2, Statistisk sentralbyrå