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Feature Article - Trend estimates and unusual real events in ABS Statistics
To reduce distortion due to the occurrence of unusual events, seasonally adjusted and trend estimates can be improved by applying appropriate prior correction to the original estimates for the unusual events. A prior correction does not change the published original estimate, but would modify the input to the seasonal adjustment process, and removes the impacts of the unusual events from published trend estimates.
A prior correction is derived by estimating the outlier for an unusual event. How to accurately identify and measure an outlier is still the subject of debate between experts in this area. For example, should the outlier be identified from the statistical characteristic of the series alone, or with the exact information from the subject matter area? ABS adopts a cautious approach using statistical methods to identify the outlier, and then uses the exact information to quantify the size of the outlier whenever possible.
If information on an unusual event is available prior to the seasonal analysis, the correction may be implemented at the period of occurrence. In many cases, however, the statistical impact has to be estimated from the time series itself and the correction cannot be implemented until further data become available. In rare occasions, a subjective decision may be needed to determine if a statistically estimated prior correction should be implemented when exact information about the cause is not available.
Unusual events may affect one or more of the three components of time series. For example, it may cause a change in the underlying movement (trend), a change to the pattern of seasonal variations (seasonality), or a short term, one-off impact (irregular). Details of such corrections are discussed below.
Large extreme value (one-off)
A large extreme irregular is an uncharacteristic movement in the original estimates. For example, the Sydney Olympics (September 2000) had a one-off effect on the overseas passenger arrivals series, and retail turnover series. This caused a one-off impact on the seasonally adjusted series. Where a one-off extreme impact is not corrected, it can distort the underlying movement as represented by the trend estimates. If prior information on the magnitude of the impact is available, a correction for the trend for the affected time points would be implemented. However, in this example, such information was not available at the time. At least one or more additional observations are normally required to help assess the one-off effect. The original and seasonally adjusted series will still contain the full impact of the large extreme value.
Trend break (permanent)
A trend break is an abrupt and sustained change in the trend path of a series between one period and another. When trend breaks occur, the ABS will correct for the permanent shift in the trend estimates, by estimating the size of the break and including it in the trend path.
Where prior information is available on the magnitude of a trend break, the size of the trend break can be factored into the trend analysis (see examples on the following page). More commonly, data for estimating the trend break may not be available at the time when the change occurs. In the absence of a reliable estimate of the impact, the ABS has to use the series to estimate, post-hoc, the magnitude of the trend break. Three or more observations after the occurrence of the trend break are needed to reliably estimate the magnitude of the trend break.
The improvement of the trend estimation will also help to improve the accuracy of the seasonal factor estimates. This will result in improved accuracy of the seasonally adjusted series. The original series and the seasonally adjusted series will still contain the full impact of the trend break.
Seasonal break (permanent)
A seasonal break is a permanent break in the seasonal pattern of a time series. Such changes occur when seasonal, trading-day and pay-day patterns change abruptly. For example, the introduction of new legislation may affect the timing of tax collections. Often they cannot be readily identified, as three or more years of data after the seasonal break are needed to accurately assess the nature of changes in seasonal pattern.
Abrupt changes to the seasonal pattern can have adverse effects on the reliability of seasonally adjusted estimates and trend estimates. Such breaks in the seasonal factors are recognised and corrected for, but usually only after at least three years have elapsed. Prior to introducing a seasonal break correction, the seasonally adjusted series and the trend series would be distorted for several years. This usually manifests itself as an episode of increased volatility in the series, until sufficient data accumulates to enable the seasonal factors to be stabilised again. The original series will still contain the full impact of the seasonal break.
HOW ARE UNUSUAL EVENTS TREATED IN THE SEASONAL ADJUSTMENT PROCESS
Different types of corrections are applied in the seasonal adjustment process, according to the nature of the event, its potential impact on the seasonally adjusted estimates and trend estimates, and the availability of information for making a correction. Four typical outcomes can occur:
1. Trend estimates and seasonal factors are allowed to continue their natural course i.e. no correction is made.
The airline pilots strike in late 1989 had a significant impact on the level of the Tasmanian passenger arrivals by air series. Figure 1 shows the seasonally adjusted and trend estimates up to and including December 1989 (when the pilots’ strike ended). At the time, there was no information available to indicate how long the strike would persist. Therefore, no correction to the trend estimates was made in any of the five months in which the strike occurred.
The seasonally adjusted time series showed a dramatic fall but was rising again towards the end of 1989. Information available at the time indicated that passenger arrival numbers would return to the previous level. The underlying nature of the time series would therefore be best represented by not intervening in the usual calculation of the trend.
FIGURE 1: TASMANIAN PASSENGER ARRIVAL NUMBERS BY AIR, 1980 TO 1989.
Figure 2 shows the same time series as in Figure 1, up to and including January 1999. Although passenger numbers fell abruptly over two consecutive months (August and September, 1989), they recovered more gradually over the following five months. A decision was made not to make any intervention. Figure 2 shows how, as more data became available during 1990, the trend adapted and now tracks the dip in activity during late 1989 well. A permanent trend break correction would have been misleading (see endnote 2).
FIGURE 2: TASMANIAN PASSENGER ARRIVAL NUMBERS BY AIR, 1980 TO 1999.
2. A correction is made for the extreme/unusual estimate after one additional original estimate becomes available i.e. no correction is made at the time of occurrence and the trend series may be suspended but a correction is inserted for the next publication.
Several large construction projects had a substantial impact on the value of Australian non-residential building approvals as shown in Figure 3. These were caused by the approval of the Melbourne Casino in June 1994, the Sydney Casino in April 1995, the Sydney Olympic Stadium in November 1996 and two new Brisbane hospitals in July 1997. Specific information on the value of these projects was available from the data collection itself, and was used to correct for the trend estimates in a timely manner. Figure 3 shows the trend series, with those corrections applied. Without this information, the trend estimates would have been distorted for several months around the period of the impact of the unusual event, as shown in Figure 4.
FIGURE 3: VALUE OF AUSTRALIAN NON-RESIDENTIAL BUILDING APPROVALS, 1994 TO 1999.
FIGURE 4: VALUE OF AUSTRALIAN NON-RESIDENTIAL BUILDING APPROVALS, 1994 TO 1999,
WITHOUT AN EXTREME CORRECTION AT JULY 1997 OR APRIL 1995.
In the case where there are very large extreme/unusual estimates, but a cause is not known, the seasonal adjustment system used by the ABS can sometimes provide an indication of an appropriate correction. If this occurs at the most recent time point, care needs to be taken to distinguish between a one off event or an emerging underlying change in the trend. If the correction cannot be reliably estimated the following options are considered:
a. no correction is applied
b. suppression of the trend estimate until a reliable estimate can be obtained.
In all cases the appropriateness of the correction is assessed against known information and by the quality of the seasonal adjustment.
3. A trend break correction may be introduced after three or more periods after the occurrence. The trend estimates may not be published prior to introducing a trend break for correction.
The introduction of The New Tax System (TNTS) in July 2000 had a permanent impact on the Retail Trade series. Prior information on the extent of the impact was not known. For the period June to November 2000 the trend estimates of the Retail Trade series were suspended because the underlying behaviour of the series could not be accurately estimated. The original and seasonally adjusted estimates were still published. The trend series was reintroduced from December 2000 after a correction to the trend estimates was made by using data up to November 2000 to estimate the permanent level shift (trend break) between June and July 2000.
Figure 5 shows the impact of the pre-GST increase in Retail trade on the seasonally adjusted estimate in June 2000. As pre-GST spending is not part of the underlying behaviour of the series, the trend would have been distorted (‘Trend before correction’) if the normal seasonal adjustment process was allowed to continue. The corrected trend (‘Trend after correction’) is also shown, where some one-off pre-GST impacts were identified and removed from the trend series.
FIGURE 5: RETAIL TRADE - TREND ESTIMATE BEFORE AND AFTER CORRECTION.
Figure 6 shows the impact of the new tax system on the seasonally adjusted and trend estimates of retail trade series in November 2000. It is important to have two different levels in the retail trade series to distinguish between the pre- and post-GST periods.
FIGURE 6: RETAIL TRADE - THE PRE-GST AND POST-GST TREND.
4. A correction for a break in seasonal factors may be introduced after three or more years of additional original estimates are available. The trend estimates and seasonal adjusted estimates are not revised prior to the correction.
Changes relating to taxation affected the Pay As You Earn (PAYE) income tax refunds series used by National Accounts. These included a change in the rate of processing refund applications for individuals in 1991 and the introduction of self assessment in 1993. These changes impacted on the seasonal pattern of PAYE refund payments as can be seen by close examination of the original data series in Figure 7 below. The seasonal peaks moved from July, August and September prior to 1992 to August and September. Figure 7 shows the corrected seasonal series, after the impact of this change had been estimated and removed. Figure 8 shows that if the breaks in seasonal patterns are not corrected for, the seasonally adjusted estimates would be subject to residual seasonality (note the peaks in July from 1991 to 1993 in the seasonally adjusted series) and increased volatility.
FIGURE 7: P.A.Y.E. REFUNDS, 1985 TO 1995, WITH CORRECTION FOR SEASONAL BREAKS
FIGURE 8: P.A.Y.E. REFUNDS, 1985 TO 1995, WITHOUT CORRECTION FOR SEASONAL BREAKS.
This paper has illustrated how the occurrence of unusual events can impact on ABS time series seasonally adjusted and trend estimates. The impact can be minimised in a timely manner if reliable prior information exists for estimating the statistical impact of the event. However, such information is usually not available and, typically, the ABS has to estimate the extent of the effect from the data itself. Prior to the correction being introduced for seasonal adjustment, there may be a period during which the seasonally adjusted estimates and trend estimates are subject to some distortion. All the prior corrections introduced are only used to produce better seasonally adjusted and trend estimates. The published original time series estimates are never altered for unusual real world events.
Some fine tuning of the corrections may be necessary even after they have been made. For example, extreme corrections may be refined when additional time periods have elapsed, or there may be a need to fit trend break correction, or seasonal break correction, once additional data is available. The appropriate treatment will depend on the nature of the impact and upon how much data and supplementary information is available.
For further information on this topic please contact Mark Zhang, Director of Time Series Analysis on (02) 6252 5132 or by email firstname.lastname@example.org.
1. A version of this article was presented as a paper to an ABS consultative forum - the Economic Statistics User Group (ESUG) in April 2003.
2. It is still subject to debate whether the transitional level changes should be included in the trend estimates.
Australian Bureau of Statistics (2003). A guide to interpreting time series - monitoring “trends”, cat. no. 1349.0, ABS, Canberra
Australian Bureau of Statistics (2001). Information Paper: Introductory Course on Time Series Analysis, cat. no. 1346.0.55.001, ABS, Canberra
Shiskin, J., Young, A. H. And Musgrave, J.C. (1967). The X11 Variant of the Census Method II Seasonal Adjustment Program. Technical Paper 15, Bureau of the Census, U.S. Department of Commerce, Washington, D.C.
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