Annex A – Seasonal adjustment of SUT quarterly series

The way in which the quarterly time series are adjusted to account for normal seasonal influences has been modified in a number of ways in this revision. This annex first provides a general explanation of the seasonal adjustment method before zooming in on the differences between the seasonal adjustment method before and after the revision. The main difference is the method used to deal with discrepancies between the sum of various seasonally adjusted series and the corresponding seasonally adjusted aggregates. This is also known as the aggregation difference.

Introduction

Seasonally adjusted time series play an important role in the interpretation of quarter-on-quarter economic developments. Seasonal adjustment is the process of removing all usual seasonal influences and calendar effects from a time series. Usual seasonal influences are all developments of a similar magnitude that occur every year during the same period, and that are expected to continue. Calendar effects are the effects of year-on-year changes in the calendar. These are mainly the number of working days per period and the effect of leap days.

Seasonally adjusted quarterly series make it possible to identify real short-term economic developments, as many economic time series show similar trends between certain quarters each year. The holiday season, for example, always leads to a spike in toy sales in the fourth quarter. When analysing toy sales in the fourth quarter of any year, it is therefore not useful to look at the unadjusted sales trend compared to the third quarter, because this will always show an increase. Adjusting for the usual seasonal influences and calendar effects gives a better picture of the state and development of the economy in any given quarter.

Seasonal adjustment method

In order to achieve an optimal seasonal adjustment of a time series, first all calendar effects are removed from the data and outliers are temporarily taken out of the series. An outlier is an observation in the dataset that does not fit statistically with the other data points, such as the purchase of a new fleet of aircraft by an airline; the value for the quarter in which this purchase takes place will be much higher than the value for a typical quarter. The quarter in question is therefore identified as an outlier, so that its value is not included in the determination of the seasonal component of the series. After preprocessing the series to correct for calendar effects and outliers, the seasonal component of the series can be determined and removed using the seasonal adjustment software X-13ARIMA.

Within the national accounts, series are published at both detail and aggregate levels. When both individual (detail) series and their aggregates are adjusted for seasonal influences separately using theaforementioned process – also called direct seasonal adjustment – aggregation differences arise: the seasonally adjusted detail series do not add up to the separately adjusted aggregate.

The reason such aggregation differences arise is that each series has its own set of outliers, ARIMA model and seasonal filters. In most cases, this is enough for differences between the detail series andthe aggregate to arise. In addition, the seasonal component of most economic series is broken down non-linearly. This means that the size of the component depends on the size of the series. As a result, the seasonal components of the subsets do not add up to the seasonal component of the aggregate.

The emergence of aggregation differences in direct seasonal adjustment is thus unavoidable, which is why international guidelines do not require seasonally adjusted aggregates to match seasonally adjusted subcomponents. However, such inconsistencies do pose challenges to users of CBS’s macroeconomic statistics. For example, a separate calculation of GDP growth through the underlying seasonally adjusted expenditure components may not match the published GDP growth figure, making it difficult to identify which spending components have driven seasonally adjusted growth. Within CBS, the choice was made to help users by minimising aggregation differences.

Old method

Before the 2021 revision, aggregation differences were minimised by adding consistency between series at several points in the seasonal adjustment process:

• GDP model settings used for other series

  The settings used for the seasonal adjustment of GDP were also used for most of the detail series. Different settings were only used in exceptional cases, when the GDP model did not fit a detail series.

• Consistent inclusion of outliers

  If an outlier was identified within a series, it was also included in the higher aggregates, with exactly the same magnitude (in absolute values). The reverse was true as well: outliers in aggregates were distributed among the underlying series. However, determining the correct distribution of these outliers and their exact value is a complex process, as the seasonal adjustment software may produce different outlier estimates for each series.

• Consistent estimation of working day effects

  A structural time series model was used to estimate a consistent working day effect across all series. ²⁾

A major challenge with this approach is that the process of determining seasonal components as effectively as possible is strongly intertwined with the process of minimising aggregation differences. It is therefore difficult to distinguish the effects of these two processes on the seasonally adjusted results. To get a better understanding of this and increase transparency, a new method is being used from this benchmark revision onwards.

New method

The premise of the new method is that seasonal adjustment and the minimisation of aggregation differences are two separate processes.

Seasonal adjustment

In seasonal adjustment, the seasonal pattern of each series is optimally removed. This means that each series (both detail series and aggregate series) gets its own settings, and that outliers and working day effects are identified separately for each series, as effectively as possible. Outliers are included here only if there is a valid economic explanation for them, and if they are statistically significant in the series. If an outlier is of low statistical significance, a valid economic explanation may still lead to its inclusion.

Sub-periodisation of the working day effect

The effect of an extra working day in a quarter has changed considerably over the years: it used to have a fairly significant impact on many economic indicators, but in today’s economy a large number of sectors operate 24/7. To account for this, the data was divided into periods of roughly nine years each, after which an assessment was made for each period as to whether there was a significant working day effect. This effect was then estimated and removed from the series. Many series still have a significant working day effect at the beginning, but almost no series still has a significant working day effect at the end.

Splitting up of the “Value added by culture, recreation and other services” series

For the value added by this branch of industry, a completely different seasonal pattern has been observed since 2007. The series has therefore been split into two parts: one from 1995 to 2007, and one from 2007 to the present. Both series have their own settings to allow for the optimal removal of the seasonal pattern, after which the two parts are merged to form one series.

Minimising aggregation differences

After individual seasonal adjustment has been applied to all series, the aggregation differences are calculated. The aggregation differences are then minimised using an optimisation model that is also used for other processes within national accounts. This is called integration. The aim of the model is to minimise the development of aggregation differences. This is important because it reduces the effect of aggregation differences on GDP trends, making it easier to determine the contribution of underlying component indicators to seasonally adjusted GDP growth.

Thus, two constraints are imposed on the optimisation method used to compile seasonally adjusted series:

1. The underlying subseries plus the aggregation difference must add up to the aggregate in each quarter.
2. Aggregation gaps between two consecutive quarters must be minimised.

Due to the second constraint, the aggregation differences for each quarter are adjusted. Because of the first constraint, this affects the seasonally adjusted subsets and aggregates. The degree of adjustment to the series is then determined by applying two criteria:

1. Proportionality: the larger the value of the series, the more the series may be adjusted.
2. Quality: the worse the quality of a series’ seasonal adjustment, the more the series may be adjusted. This quality is assessed by the seasonal adjustment software.

The extent to which aggregation differences between two consecutive quarters must be reduced is determined in consultation with relevant experts. An assessment is also made to determine the extent to which both criteria (proportionality and quality) for distributing aggregation differences among the series must be taken into account.