3401.0 - Overseas Arrivals and Departures, Australia, 2004  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 14/09/2004   
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Feature Article - Seasonally adjusted and trend estimates - adding value to the analysis of short term movements


The Australian Bureau of Statistics (ABS) adjusts short-term overseas arrivals and departures (OAD) statistics to account for seasonal and irregular factors. The original, seasonally adjusted and trend series differ from each other in important respects, and these differences need to be understood so that they can be used effectively.

This article explains the key differences between the original, seasonally adjusted and trend time series. In doing so, it explains why the ABS recommends that users of OAD statistics use trend estimates for analysing and interpreting the underlying behaviour of OAD. This article also discusses the benefits and disadvantages of some of the commonly used indicators (measures) of OAD behaviour and provides guidelines for interpreting time series estimates.


Original time series

Original estimates are the actual estimates the ABS derives from data provided by persons entering or leaving Australia. Movements in the original series can be attributed to the combined impact of systematic calendar related influences, irregular influences and the underlying (trend) direction in behaviour.

The systematic calendar related influence represents the combined effect of seasonal cycles, trading day patterns and moving holidays. Each of these influences has one characteristic in common – they operate in a sustained and systematic manner that is calendar related. Some examples of such influences include the large increase in travel during December as a result of the Christmas holiday period, or the increase in visitor arrivals from Singapore and Hong Kong during Chinese New Year (held in January or February).

Irregular influences come from events or activities that are neither systematic nor predictable. They include the short-term phenomena that temporarily impact on OAD. Examples of such influences include:

  • dramatic fluctuations in the Australian dollar
  • war or terrorist attacks
  • special events (e.g. Olympic Games or International Exhibitions) held in Australia.

Sampling and non-sampling errors that behave erratically with no noticeable systematic pattern are also considered irregular influences.

Trend movements refer to the underlying behaviour of the series and results from such influences as population growth or general economic changes.

Seasonally adjusted time series

Seasonally adjusted estimates are derived by estimating and then removing systematic calendar related influences from the original series. This is applied to reveal the underlying non-seasonal features of a series. Therefore, this series represents the net effect of irregular influences and the underlying trend.

Trend time series

Trend estimates are derived by using the seasonally adjusted series and dampening any irregular influences. These estimates reveal the long term movement of the series without calendar related and irregular effects. Therefore, this series represents the underlying level of OAD, which help analysts to tell whether short-term movements are increasing, decreasing or steadying.


The ABS publishes summary measures for the original, seasonally adjusted and trend series in the key figures of this publication. Monthly and annual percentage changes can be calculated for all three time series. Changes in original and seasonally adjusted series can produce inconsistent and occasionally contradictory signals about developments in the underlying long-term direction of the series. As a result, users may be confused about the direction of the series and which series is the best to use for their purposes.

Table 1 summarises the benefits and disadvantages of the various measures used to monitor OAD and provides guidelines for interpreting OAD time series.

One of the commonly used indicators of OAD behaviour has been to calculate the change in the original estimates for the current month compared with the same month a year earlier (year apart change). This is not the best measure of the long-term direction of OAD due to the contribution of seasonal and irregular factors to the original estimates. For example, according to original estimates, short-term visitor arrivals during May 2004 increased by 31% compared with May 2003. This rate of change presents a misleading picture of growth as it does not take into account calendar dynamics (i.e. changing patterns in seasonality and trading day variability), nor the impact of irregular influences such as Severe Acute Respiratory Syndrome (SARS) and the war in Iraq.

Sub-annual aggregates of monthly original data (e.g. quarterly and year-to-date aggregates) may also present a misleading picture of growth in the series and will delay the identification of turning points in the monthly series.

Trend estimates are much better for analysing and monitoring the underlying behaviour in OAD than original and seasonally adjusted estimates. However, as shown in table 1, there are weaknesses associated with the trend series which need to be kept in mind.

Time seriesMonth to month percentage change Year apart percentage change

The seasonal influence is likely to be the dominating factor in the variation in monthly original OAD estimates.

While the original estimates are useful in understanding the actual number of movements for a given period of time, due to the presence of seasonal and irregular factors they should not be used for time series analysis.

While this measure performs a crude seasonal adjustment by reducing the impact of constant yearly seasonal influences, in practice, these effects are rarely eliminated due to trading day influences and changing patterns in seasonality. This measure may also be highly affected by irregular influences.

This measure should only be used if seasonally adjusted or trend estimates do not exist for a given series. In such cases great caution must be applied.
Seasonally adjustedBenefits
A reasonably good measure for the underlying short-term variation (i.e. impact of one-off events) in the original estimates. This measure may also provide supplementary information to assess future trend estimates.

In many instances, the irregular component dominates the overall monthly movement in seasonally adjusted OAD estimates.

For some OAD series, caution should be applied when interpreting this measure of change due to the volatile nature of the irregular component. This measure should only be used when there is a need to focus on and respond to irregular factors.

This measure should not be used because of the potentially high contribution of the irregular factor to the seasonally adjusted movement, thus masking the underlying behaviour.
This is the best measure of the underlying, long-term direction of an OAD series.

The measure provides a smoothed historical perspective of the underlying pattern of OAD behaviour without the impact of calendar related or irregular influences. Users are able to monitor the level and shape of turning points over time, aiding timely and informed decision making.

Trend estimates are subject to revision (principally recent months).

Caution must be applied when interpreting the underlying direction for recent months. Revisions to the trend series at the current end will occur due to additional original information becoming available. For instance, in order to confirm the presence of a turning point, approximately three monthly observations will be required.
This measure provides an approximation of the average trend movement over the year.

The measure of change may not reflect the current trend movement or pattern of behaviour. For instance, key monthly turning points that occurred during the year will be missed.

Be aware of any turning points that may have occurred during the year.


Seasonally adjusted and trend estimates add to the understanding of OAD statistics. Seasonally adjusted estimates allow users to analyse short-term irregular impacts on the series, while trend estimates provide a better method to analyse and monitor the underlying direction of OAD.

The ABS recommends that users carefully assess whether they are making the best use of the OAD estimates made available to them, and whether their current analyses are revealing true trends in OAD. In most cases, the trend series is the best source of information on the long-term direction of these statistics.


For a more detailed discussion and analysis of OAD time series estimates, see the ABS Demography Working Paper 2004/2 – Interpretation and Use of Overseas Arrivals and Departures Estimates (cat. no. 3106.0.55.002), available on the ABS web site. This working paper explores time series concepts in more detail and uses the example, short-term visitor arrivals to Australia from Japan to demonstrate the effect that calendar related and irregular factors can have on original estimates.