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Introduction

A3.1 Quarterly time series such as those in national accounts publications are affected by three influences - calendar ( mostly seasonal), trend and irregular. When interpreting a quarterly series, it is often helpful to take account of the seasonal and other regular calendar-related influences. The seasonal adjustment process removes these influences, and the remaining (seasonally adjusted) series reflects the trend and irregular influences. The irregular component refers to changes attributable to irregular events such as industrial disputes or lumpy investments. A further statistical process (Henderson smoothing) removes the irregular influence to reveal the trend. This appendix summarises the methods used by the ABS to decompose quarterly national accounts series into their three components.


The seasonal adjustment process

A3.2 Seasonal effects usually reflect the influence of the seasons themselves, either directly or through production series related to them (such as farm production), or social conventions (such as the incidence of holidays) or administrative practices (such as the timing of tax payments). Other types of calendar variation occur as a result of influences such as the number and composition of days in the calendar period (trading day), accounting or recording practices adopted by businesses, the effect of regular paydays on activity levels or the incidence of movable holidays (such as Easter).

A3.3 Statistical techniques can be used to evaluate the effects of normal seasonal and other calendar influences operating on a series. If significant stable seasonal or calendar variation is detected, then the estimated effects may be removed from the series to produce a seasonally adjusted series. Although stable calendar variation may be present in a series, factors applying in a particular period may vary significantly from year to year due to the variability in the number and composition of days in that particular period. This is especially evident in series affected by, say, the payment of salaries or pensions on a fortnightly basis.

A3.4 Not all statistical series are significantly affected by seasonal or calendar influences which are regular enough to be described as 'stable', so seasonal or calendar influences cannot always be removed from them. In such cases the original series may be regarded as also being the seasonally adjusted series. Some examples in the quarterly national accounts are the rent component of farm costs and the series related to the consumption of fixed capital.


The method of seasonal adjustment

A3.5 The ABS method of seasonal adjustment is the SEASABS (SEASonal analysis to ABS standards) package, a knowledge-based seasonal analysis and adjustment tool. The seasonal adjustment algorithm used by SEASABS is based on the X-11 ARIMA package from Statistics Canada. This in turn is based on the United States Bureau of the Census Method II Seasonal Adjustment Program, X-11 Variant. In the X-11 method, calendar effects, where measurable, are estimated using mainly filtering techniques, and occasionally regression procedures. In certain cases (such as the payment of pensions) additional information may be used to estimate appropriate prior adjustment factors. The estimated seasonal and calendar influences, together with certain prior adjustment factors, provide the combined adjustment factors by which the original series is seasonally adjusted.

A3.6 The X-11 technique proceeds by decomposing the series to be analysed into estimated trend, seasonal and irregular components. The irregular component reflects the influence of unusual or transitory effects, e.g. the effect of a major industrial dispute or of unseasonal weather conditions. It also reflects sampling and non-sampling errors which may be present in the original series. The X-11 program includes a statistical procedure for identifying and discounting unusually large or small values included in the original series. Supplementary information is used to assess the results produced by this technique. Occasionally, prior modification of extreme values is undertaken, again using supplementary information, in order to better allow for these influences. This procedure minimises the extent to which the estimated seasonal component is affected by irregular influences. It should be noted that only the estimates of seasonal and/or other types of calendar variation are removed from the original series to form the seasonally adjusted series. Since the irregular influences remain, an unexpectedly large movement in the seasonally adjusted series does not necessarily indicate a change in the underlying trend of the series.

A3.7 Adjustments are also made prior to seasonal analysis to deal with abrupt discontinuities in the seasonal pattern or the trend where sufficient observations are available to estimate the magnitude of the effects. These 'break factors' have been employed retrospectively in the analysis of a number of national accounts series, and some series contain more than one such break. However, it is impossible in most cases to recognise and assess changes in seasonality or trend at the time they occur. The seasonal adjustment process alone cannot indicate whether an unexpected movement appearing in current seasonally adjusted figures denotes a variation in trend, or an unusual (irregular) effect, or whether it is due to an abrupt change in seasonality.


Additive, pseudo-additive or multiplicative adjustments

A3.8 The SEASABS program allows for the original series to be decomposed into trend, seasonal and irregular components by using a multiplicative, additive or pseudo-additive model. The choice of which of these models to use depends on whether it is more appropriate to consider the amplitudes of the trend, seasonal and irregular components to be proportional to or largely independent of each other. Specifically, the multiplicative model treats all three components as dependent on each other, the additive model treats them independently, and the pseudo-additive model treats the seasonal and irregular components as independent of each other but dependent upon the level of the trend.

A3.9 Although most series in the ANA are adjusted multiplicatively there are some exceptions. Series which include both positive and negative values cannot be directly adjusted using a multiplicative model. If such series cannot be disaggregated into components having wholly positive (or negative) values, an additive or pseudo-additive model must be used. Several series relating to gross farm product (i.e. outputs and inputs) are affected by such extreme seasonal variations that the pseudo-additive model provides the best seasonally adjusted results. Other time series (especially inventories) are best adjusted using the additive model.


Direct or aggregative adjustments

A3.10 It is possible to seasonally adjust an aggregate series either directly or by seasonally adjusting a number of its components and adding the results. The latter (aggregative) method has been employed for most of the major aggregates in the national accounts. Besides retaining, as far as possible, the essential accounting relationships, the aggregative approach is needed because many of the aggregates include components having different seasonal and trend characteristics, and sometimes require different methods of adjustment. Details of the methods of adjustment used for each of the quarterly national accounts aggregates are available on request.


The annual seasonal reanalysis cycle and revisions

A3.11 National accounts series are normally reanalysed annually using data consistent with the June quarter national accounts estimates. On occasions, however, particular components have been reanalysed before the normal time because of one or more of the following conditions:

• there appear to have been significant changes in seasonality;

• major revisions to annual estimates are made which also affect quarterly movements; and/or

• changes have been made to the detailed way in which the seasonal adjustment process has been carried out.

A3.13 The following points need to be taken into account when using seasonally adjusted statistics:

• seasonal adjustment is a means of removing the estimated effects of seasonal and other types of calendar variations from statistical series, so that the effects of other influences on the series may be more clearly recognised;

• seasonal adjustment does not remove the effect of irregular influences from the statistics, so an unexpected movement in a seasonally adjusted series should not necessarily be regarded as a change in trend; and

• seasonally adjusted statistics will be revised following revisions to the original data and as additional original data points are included in the analyses each year.

A3.15 In cases where the removal of only the seasonal element from a seasonally adjusted series may not be sufficient to allow identification of changes in its trend, a statistical technique is used to damp the irregular element. This technique is known as smoothing, and the resulting smoothed series are known as trend series.

A3.16 Smoothing, to derive trend estimates, is achieved by applying moving averages to seasonally adjusted series. A number of different types of moving averages may be used; for quarterly series a seven term Henderson moving average is applied. The use of Henderson moving averages leads to smoother data series relative to series that have been seasonally adjusted only. The Henderson moving average is symmetric, but asymmetric forms of the average are applied as the end of a time series is approached. The application of asymmetric weights is guided by an end weight parameter which is based on the calculation of a noise-to-signal ratio (much like the 'I/C ratio' in X-11). While the asymmetric weights enable trend estimates for recent periods to be produced, they result in revisions to the estimates when subsequent observations are available.

A3.17 Revisions to the trend series may arise from four factors:

• the availability of subsequent data;

• revisions to the underlying data, especially in more recent periods;

• re-estimation of seasonal factors; and

• asymmetries in the smoothing procedure.