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Seasonally adjusted estimates are derived by estimating and then removing the systematic calendar related influences from the original series. Concurrent seasonal adjustment methodology is used to produce OAD seasonally adjusted estimates. This means that data from the current month are used in estimating the calendar related influences for the current and previous months. This method continually fine tunes the estimates whenever new data becomes available. The seasonally adjusted series reveals the underlying non-seasonal features of a series, and will still contain irregular factors which can potentially mask the underlying direction of the series.
Trend estimates are derived by using the seasonally adjusted estimates and then dampening any irregular influences. This is done by applying a 13-term Henderson-weighted moving average to all months of the respective seasonally adjusted series except the first and last six months. The trend estimates are created for the last six months by applying surrogates of the Henderson weighted moving average to the seasonally adjusted series. This results in estimates that provide an improved measure of the fundamental or underlying level of the series. These trend estimates help analysts to tell whether short-term movements are increasing, decreasing or steadying.
For a more detailed description of time series methods, see the Information Paper, An Introductory Course on Time Series Analysis (cat. no. 1346.0.55.001).
SYSTEMATIC CALENDAR RELATED INFLUENCES
Calendar related influences come from events that occur in a regular or predictable manner. There are three types of systematic calendar related influences on original estimates: seasonal, trading day and moving holiday influences.
Seasonal influences comprise the most common calendar related behaviour, where a cyclical pattern evolves (typically in annual cycles) as a result of fixed calendar related events or changes in the seasons. For example, historically March, February, August and December have the most short-term visitor arrivals from Japan. These peaks coincide with traditional Japanese holidays, as well as annual celebrations such as Obon (a Buddhist celebration in August) and New Year festivities (early January). Increases in visitor arrivals during December may also reflect the differing climates between the two countries, with Japan in the midst of their winter.
Trading day influences refer to the impact on the series as a result of the number and type of days in a particular month. Each day of the week can occur a different number of times from month to month and year to year. If more activity generally occurs on some days of the week than others, the number of times each day occurs within each month will have an impact on the behaviour of the monthly series. For example, if more visitor arrivals from Japan arrived in Australia on Saturdays, a month containing five Saturdays will have more visitor arrivals from Japan than other months in the absence of other influences.
Moving holiday influences derive from holidays or events which do not occur on a fixed calendar day from year to year. In particular, they may occur in different months and so impact on the level of activity for the month in which they fall. For example, Chinese New Year is a moving holiday which is usually observed in February but sometimes in January, depending on the lunar calendar. This holiday generally results in increased visitor arrivals and resident departures from/to several Asian countries including Singapore and Hong Kong. Easter is another example of a moving holiday, which normally falls in April but sometimes in March. Such moving holidays result in a non-annual calendar related influence.
For more information on how the ABS adjusts the original series for calendar related influences, see the Time Series Frequently Asked Questions web page, available on the ABS web site.
Irregular influences come from events or activities that are neither systematic or predictable. Irregular influences may reflect the short-term phenomena that temporarily impact on short-term movements to and from Australia. Examples of such influences include one-off events such as dramatic fluctuations in the Australian dollar, changes in air fares, war or terrorist attacks, or special events (e.g. Olympic Games or International Exhibitions) held in Australia. Irregular influences often contribute to a large proportion of the non-systematic volatility observed in the behaviour of a series.
For instance, during the first half of 2003 fewer than usual Japanese visitor arrivals came to Australia. This may have resulted from the impact of Severe Acute Respiratory Syndrome (SARS) and the anticipation and commencement of military action in Iraq. Similarly, visitor arrivals from Japan also troughed in November 2001, coinciding with the after-effects of the 11 September 2001 terrorist attacks in the United States of America.
Sampling and non-sampling errors that behave in an erratic fashion with no noticeable systematic pattern are also irregular influences.
For more information on how the ABS adjusts the seasonally adjusted series for irregular influences, see the information paper, A Guide to Interpreting Time Series–Monitoring Trends (cat. no. 1349.0).
CASE STUDY – DECOMPOSING ESTIMATES FOR SHORT-TERM VISITOR ARRIVALS TO AUSTRALIA FROM JAPAN
As with all time series data, movements in the original estimates for short-term visitor arrivals to Australia from Japan can be attributed to the combined impact of systematic calendar related factors, irregular factors and trend movements.
The following sequence of graphs presents the monthly time series decomposition of short-term visitor arrivals to Australia from Japan for the past decade. Graphs 1 to 7 illustrate the contribution of the seasonal, trading day, irregular and trend factors to the behaviour of the original series.
The original estimates for short-term visitor arrivals to Australia from Japan are presented in graph 1. It shows that there are variable patterns of movement for particular months and periods of time. By decomposing the series we can determine the contribution of calendar related (i.e. seasonal and trading day) and irregular influences, as well as determine whether the underlying trends for travellers from Japan to visit Australia are stable, increasing or decreasing.
During June 2004, the original series shows that there were 46,100 short-term visitor arrivals to Australia from Japan.
Graph 2 presents the approximate contribution of seasonal factors to the original estimates for short-term visitor arrivals from Japan. From this graph we can see that the series has a strong seasonal pattern of behaviour, with March, August, February and December consistently peaking for visitor arrivals from Japan during the past decade. These peaks may be attributed to traditional Japanese holiday periods and celebrations held during these months. Seasonal lows are also consistently recorded for June and May.
This graph also illustrates the evolving nature of seasonal patterns over time. For instance, over the past decade the month of January has changed from seasonally high (i.e. above the neutral line of 1.00) to seasonally low. Similarly, while December continues to record seasonally high movements, this influence has been diminishing over the past decade.
During June 2004, the seasonal factor was 0.86, indicating that for June 2004 short-term visitor arrivals from Japan were seasonally low by 14% (below neutral, 1.00).
Graph 3 presents the approximate contribution of trading day factors to short-term visitor arrivals from Japan. This graph has been scaled differently to graph 2 to enable this influence to be seen clearly. It is evident that trading day factors have had less influence on short-term visitor arrivals from Japan during the past decade than seasonal factors.
From this graph we can see a trading day affect arising from the different number of days in each month (i.e. some months have 28, 29, 30 or 31 days). For instance, the troughs in this graph represent the month of February (for non-leap years) which is the shortest month of the year (28 days). For leap years, there is less trading day affect during February as a result of the extra day (29 days).
Graph 4 presents the combined contribution of seasonal and trading day factors, that is, the systematic calendar related factors on short-term visitor arrivals from Japan. From this graph it is evident that the underlying behaviour of the original series is indeed masked by calendar related influences.
The seasonally adjusted series (graph 5) is obtained by estimating and then removing the seasonal, trading day and moving holiday factors from the original series.
The seasonally adjusted series reveals the non-seasonal features of the series and presents the net effect of the two remaining distinctly different behaviours: the irregular short-term factors and the underlying trend. In order to reveal the underlying long-term direction of the series we need to remove the irregular factors from the series.
Graph 6 presents the approximate contribution of irregular factors to short-term visitor arrivals to Australia from Japan. This graph shows that unlike the calendar related factors, the irregular factors do not display any consistent pattern of behaviour. Generally, the irregular factors have also had less impact on the original series for short-term visitor arrivals from Japan than the calendar related influences. However, in recent years a number of one-off events have had a large impact on short-term visitor arrivals from Japan.
For instance, November 2000 recorded the largest positive irregular influence in the series since this data has been collected. At this time the irregular factor was estimated as 1.20, indicating the seasonally adjusted estimate was 20% above the trend. This may be associated with new or deferred travel following Sydney hosting the 2000 Olympic Games in September/October 2000.
Conversely, the largest negative irregular influence occurred in May 2003 when the irregular factor was estimated as 0.56, indicating the seasonally adjusted estimate was 44% below the trend estimate. This may reflect the significant impact of SARS and the war in Iraq.
The irregular factors are often thought of as distractions for many time series purposes, as they have a short-term affect on the series which mask the underlying behaviour of the series.
Graphs 1 to 6 have illustrated the volatile nature of the original and seasonally adjusted time series of short-term visitor arrivals from Japan. Graph 7 presents the trend of short-term visitor arrivals from Japan. These estimates are calculated by smoothing the seasonally adjusted series. It represents the best estimate of the underlying direction of the series, as it excludes calendar related and irregular influences. This graph indicates that since October 2003 short-term visitor arrivals to Australia from Japan have been declining.
The June 2004 trend estimate for short-term visitor arrivals from Japan (55,447 movements) is obtained by applying a specific set of weighted moving averages to the seasonally adjusted estimate and can be thought of as resulting from dividing the seasonally adjusted estimate (54,805 movements) by the irregular factor (0.988421) prior to rounding.
APPROPRIATE USE AND INTERPRETATION OF TIME SERIES ESTIMATES
The ABS publishes summary measures of the original, seasonally adjusted and trend series in the key figures of OAD publications. Monthly and annual percentage changes can be calculated for all three series, which can produce inconsistent and occasionally contradictory signals about developments in the underlying direction of OAD. As a result of these inconsistent signals users may be confused about the direction of the series or which series they should be using 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.
MONTH TO MONTH MEASURES OF CHANGE
As demonstrated above, calendar related factors are likely to be the dominating factor in the monthly variation in the original series. Similarly, in many cases the irregular factor may highly affect the monthly variation in the seasonally adjusted series. For instance, in 106 of the last 120 monthly movements for short-term visitor arrivals from Japan, the irregular component contributed more than the trend movement to the monthly variation in the seasonally adjusted series. Such factors make the underlying direction of the original and seasonally adjusted series difficult to interpret with confidence.
Users wishing to analyse and monitor the underlying behaviour of the series should analyse the month to month movements in the trend series. While trend estimates at the current end of the series are subject to revision (due to additional original information becoming available), these latest trend estimates nonetheless provide a more timely and reliable indication of the underlying direction of OAD than the original or seasonally adjusted series.
YEAR APART MEASURES OF CHANGE
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 the outbreak of Severe Acute Respiratory Syndrome (SARS) in several Asian countries 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 direction of OAD than original and seasonally adjusted estimates. However, caution should be exercised when using trend annual percentage changes as it only an approximation of the long-term movement in the series, and unlike the month to month measure, it may not reveal turning points that occur during the year.
TABLE 1: BENEFITS AND DISADVANTAGES OF VARIOUS MEASURES OF OAD BEHAVIOUR
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 statistics. In most cases, the trend series are the best source of information on the underlying long-term
direction of these statistics.
For further information on OAD time series estimates, contact Chrissy Beruldsen on Canberra (02) 6252 5640, email firstname.lastname@example.org.
Australian Bureau of Statistics, 2003, A Guide to Interpreting Time Series–Monitoring Trends, cat. no. 1349.0, ABS, Canberra.
Australian Bureau of Statistics, 2000, Information paper: An Introductory Course on Time Series Analysis, cat. no. 1346.0.55.001, ABS, Canberra.
Australian Bureau of Statistics, 1993, Information paper: Introduction to Concurrent Seasonal Adjustment into Retail Trade Series, cat. no. 8514.0, ABS, Canberra.
Australian Bureau of Statistics, Overseas Arrivals and Departures, Australia, cat. no. 3401.0, ABS, Canberra.
Australian Bureau of Statistics, 'Smarter Data Use', Australian Economic Indicators, March 1992, cat. no. 1350.0, ABS, Canberra.
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