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UNDERSTANDING AND USING TIME SERIES ESTIMATES
Seasonal effects and identifying seasonality
Seasonal effects are predictable, calendar related effects that happen the same way, at the same time every year, or sometimes recur a few times a year. Seasonal effects are fairly stable with respect to timing (when they happen), direction (whether the data fluctuates) and magnitude (by how much the data fluctuates). For example, consumers tend to increase their retail spending at Christmas, meaning that retail sales go up in December and drop back down again in January. Another example of a seasonal effect is the increase in water consumption during summer due to warmer weather.
Some seasonal effects are not precisely annual, however their timing can still be predicted. These seasonal effects are known as moving holidays or trading day effects. Easter is a moving holiday as the date at which Easter occurs changes every year, however the date it will fall on can be predicted in advance. As Easter sometimes falls in March and sometimes in April, the change in months can have a large effect on the activity for certain series, such as tourist accommodation.
A trading day effect relates to the number of times that each day of the week occurs during any given month. As different days of the week often have different levels of activity, the observed figure for any month may include the effect of having certain extra days. For example, in Australia, generally more cars are sold on Wednesdays than on Saturdays (ABS, Customised report, 2010). Therefore, any month which contains five Wednesdays is more likely to have higher sales than other months with five Saturdays.
Seasonality in an original time series can be identified by regularly spaced peaks and troughs which have a consistent direction and approximately the same magnitude every year. The graph below depicts a strong seasonal series. There is an obvious large seasonal increase in retail sales in Victoria each December, due to Christmas shopping. The magnitude of the seasonal component stays fairly consistent, while the underlying direction of the data increases over time. A trading day effect can also be observed in the graph, with a dip in turnover occurring each February. This lower level of retail activity is due to February having fewer days than other months.
Seasonal adjustment is an analytical technique that estimates and then removes seasonal effects from an original series. Original data need to be seasonally adjusted in order to reveal to analysts an estimate of the true underlying movement in the series (the trend), as well as certain non-seasonal characteristics (irregular components). Removing seasonal patterns can help analysts better understand what has been happening to the data by enabling them to see the effects of other non-seasonal influences.
Similar to the graph above, the graph below also highlights retail turnover in Victoria, however the seasonal component in the original series has been estimated and removed to form the seasonally adjusted series. As a consequence, the peaks in December retail sales have been smoothed out due to the seasonal adjustment process, leaving just the underlying direction of the data (the trend) and any irregular component.
Any series that contains seasonal patterns should be seasonally adjusted in order to be able to identify the underlying direction of the data. However, if the data has a very strong irregular component or has weak seasonal patterns it may be difficult to seasonally adjust. This means that the seasonal patterns will be harder to identify and the seasonally adjusted estimates will be less reliable. In these cases, the ABS will issue a caution with the published data.
The irregular component results from short term fluctuations in the data which are neither systematic nor predictable. The irregular component can also be referred to as the residual component, or the volatility or noise in a series.
Most time series contain some degree of volatility or noise, causing original and seasonally adjusted values to fluctuate around the general trend level. For example, crop yields are naturally volatile due to factors such as the weather. The impact of the irregular component can be seen in a seasonally adjusted series, but is smoothed out of a trend series in order for the underlying direction of the data to be identified.
Highly volatile series contain almost no regular patterns, meaning they are dominated by their irregular component. This can make it very difficult to identify the seasonality and trend, and thus to gain an understanding of what has been happening to the data over time. An example of a very irregular series can be seen in the graph below. It is difficult to tell from the graph whether the short term movements in the value of non-residential building approvals in Victoria is caused by seasonal or irregular influences. This is why the ABS does not publish seasonally adjusted estimates for the value of non-residential building approvals in Victoria.
The trend component is defined as the long term movement in a series. The trend highlights the underlying direction of the data, and is formed once the irregular components have been smoothed out of the seasonally adjusted series. The underlying direction is typically driven by influences such as price inflation (for time series in current prices only), population growth, general economic development and changing consumer habits. Trend estimates are usually directly comparable at different points in time as they have had any seasonal effects and short term fluctuations removed. Trend estimates are revised as new original estimates become available. This is to ensure that the ABS is providing the most up-to-date and best possible estimate.
The graph below again highlights retail turnover in Victoria. The graph shows a strongly seasonal original series, and a seasonally adjusted series with a few irregular components. The trend series shows the general long term movement of the data in the absence of any seasonal and irregular effects. The graph shows that despite some slowing in the trend growth around 2004 and 2005, monthly retail turnover in Victoria has been gradually and steadily increasing over the past ten years.
When to use different types of time series estimates
Time series data may be available as original, seasonally adjusted or trend estimates. Therefore it is important to understand that these three separate indicators all describe different aspects of the same data, and are useful for different analytical purposes.
Original estimates are the best estimates that can be made of the level of activity at any particular point in time. As the original series contains all three time series components it can be useful for identifying peaks and troughs around which business or government may wish to plan. For example, in the graph below, the peaks in the retail clothing original series may be of use to employers for forecasting when busy periods are likely to occur in the future, allowing them to roster on extra staff or to order more stock.
Residual noise, seasonal patterns and the underlying direction of the series make it difficult to compare original estimates at different points in time. If month-to-month movements are compared using an original series, seasonal effects will often be seen, and they will usually dominate any month-to-month movement. In the original series in the graph above, the clothing sales go up in December and drop back down again in January. If a month-to-month comparison was made from December to January it would seem reasonable to say that retail clothing sales underwent a large decline. However, once the seasonally adjusted and trend estimates are derived, it can be seen that the retail clothing sales have been predominantly increasing over time.
In general, original estimates should not be used to calculate year-to-year movements. This is because a comparison of original data from the same period each year does not completely remove all seasonal effects. Moving holidays, such as Easter and Chinese New Year, fall in different periods each year, hence they will distort observations. For example, Easter occurs in April for most years, but if Easter falls in March, the level of activity can vary greatly for that month for some series. A comparison of different time points using original estimates will also ignore trading day effects if the two periods have different compositions of trading days.
There are occasions when original data is suitable for making specific comparisons, such as when the user is wanting to measure the effects of seasonality. Examples include:
Seasonally adjusted estimates
Seasonal patterns are removed from seasonally adjusted data, however residual noise and irregular influences are still present. Seasonally adjusted estimates can be used to compare period to period changes, however, they are recommended to be used with caution due to residual noise still present in the series.
Seasonally adjusted estimates are useful when the user is trying to measure the impact of an irregular event, such as 'was that advertising campaign effective in increasing sales?'. As the seasonal component has been removed, only the underlying direction and the irregular component remains. If a larger than normal irregular component was observed in the month that the advertising campaign was running, then it could be a good indicator that the campaign was effective in increasing sales. However, it is important to keep in mind that it may not have been the only factor contributing to an increase in sales. It is also a good idea to compare the seasonally adjusted series with the trend series when investigating the impact of irregular events.
The trend captures the long-term behaviour of the series, as well as the various medium-term business cycles. In contrast to an original series, or a noisy seasonally adjusted series, the trend does not frequently change direction from period to period and in fact, trend movements are generally quite smooth and gradual in comparison.
As such, trend estimates are directly comparable at different points in time, making them the most appropriate estimate for comparing month-to-month and quarter-to-quarter changes. Trend estimates are also the most suitable option for comparing year apart changes. However, it is important to note that recent estimates, typically the last three or four, may be revised as new original estimates become available.
The graph above, liquor retailing in Victoria, shows the original, seasonally adjusted and the trend series. Strong seasonal factors can be seen in the original series around October, November and peaking in December. These seasonal cycles have been estimated and removed in the seasonally adjusted series, but some volatility still remains. Both the seasonal cycles and the volatility have been removed from the trend series. While the original series would be useful for identifying the peak periods in liquor retailing in Victoria, period to period comparisons would not tell an accurate story of what the liquor retail market is doing over time. Thus it is better to use the seasonally adjusted, and preferably the trend series to compare changes in the level of activity for different time periods.
Analysis advice for all types of estimates
When comparing year-to-year data, regardless of the type of time series estimate being used, a major disadvantage for analysts are time delays in the identification of turning points. Turning points occur when the direction of the underlying level of the series changes, for example, when a consistently decreasing series begins to rise steadily. In making year-to-year comparisons, a rise in a previously decreasing series may not be identified until it has actually been rising for quite some time. For more information, refer to Information Paper: A Guide to Interpreting Time Series - Monitoring Trends, 2003 (cat. no. 1349.0).
It is also important to note that for some analysis questions, more than one type of series may need to be considered. For example, few retailers would hire large numbers of new staff in late December, because they can see from looking at a typical retail turnover original series, that historically sales decrease in January. However, they may look at the trend or seasonally adjusted series to plan for the employment of additional staff throughout the year, if the underlying direction of retail sales has been increasing.
Other considerations for analysing time series estimates
There are many important points and issues which need to be considered when conducting time series analysis. Some key areas are discussed below.
Stock and flow series
Original, seasonally adjusted and trend time series estimates can be classified into two different types: stock and flow. Stock series are measures of activity at a point in time and can be thought of as 'stocktakes'. For example, the Monthly Labour Force is a stock measure because it takes stock of whether a person was employed or unemployed in the reference week. Other examples of stock series include inventories and estimated resident population.
Flow series are a measure of activity over a period, such as the number of bicycles sold in a month. Manufacturing is a flow measure because a certain amount of product is produced each day. These amounts are then summed to give a total volume of production for a given reporting period. Other examples of flow series include retail trade, balance of payments, housing finance and capital expenditure. Flow series often contain trading day effects, for example, one month in a series may contain five Saturdays and another month may contain five Wednesdays, which may impact on the level of activity for each month. These trading day effects have been removed from ABS seasonally adjusted and trend estimates, but remain in the original estimates.
Although a time series is a collection of consistently measured data items, sometimes real world effects can occur which result in an abrupt change to the level of activity in a series. This is called a structural break, or can often be referred to as a trend break.
A trend break is an abrupt but sustained change in the underlying level of a trend series. In general, a change needs to be reflected by at least six months or three quarters of raised or lowered levels in order to be considered a trend break. If the span of the deviating values is shorter than this period, then they can be classified as extreme values. Such changes in the level of a series are of concern for time series analysis as they can distort trend estimates of surrounding time periods if a trend break is not inserted. Trend breaks are inserted into, and identified within, published ABS trend estimates as required.
A trend break may be caused by:
The trend series in the graph below shows that when the GST was introduced in July 2000, there was a sudden drop in the general level of retail turnover in electrical and electronic goods retailing in Victoria. This drop in activity was identified as a trend break as the lowered retail turnover levels continued for longer than six months.
The seasonal adjustment process used by the ABS allows for moving seasonality in a time series; that is a gradual evolution of seasonal patterns over time. However, an abrupt and permanent change in the seasonal pattern is known as a seasonal break, which the ABS identifies and corrects. Seasonal breaks are generally caused by changes in the coverage of a survey, social traditions, administrative practices or technological innovations. In the absence of external information quantifying the change in seasonality, at least three years of data is required before a seasonal break can be confirmed and a correction can be made.
When a seasonal break occurs, the surrounding seasonal factor estimates are distorted unless a correction is applied. An uncorrected seasonal break can result in some seasonality remaining present in the seasonally adjusted estimates. Seasonally adjusted estimates in the region of an uncorrected seasonal break may appear more volatile; and since the trend is derived from the seasonally adjusted series, trend estimates may be indirectly distorted.
Most time series contain some level of noise or volatility. On occasions when the degree of irregularity is unusually large, the values can deviate from the trend by a large margin, resulting in an extreme value. Some examples of the causes of extreme values include adverse natural events (floods), industrial disputes, or the implementation of a new government policy.
Extreme values need to be identified and corrected so that they do not distort the path of the trend series. The trend series is intended as a measure of underlying direction, or long term growth, so it is not desirable for it to respond to one-off, irregular movements.
In the graph below, the seasonally adjusted series for retail turnover in department stores in Victoria is quite volatile with many irregular values. Several large extreme values can be seen in the seasonally adjusted series in late 2008 and early 2009. These irregular values were due in part to people spending their government economic stimulus payments. As these extreme values were attributed to real world effects and were considered abnormal, they have been removed from the trend estimates, meaning the trend series does not rise and fall with these irregular values and they do not form part of the underlying direction.
Revisions to time series
Seasonally adjusted and trend estimates routinely get revised as new estimates become available. For example, the trend estimates for retail trade for December 2010 will be revised as information is collected for January 2011, and again when information is collected for February 2011. For both monthly and quarterly series, once three cycles have passed revisions to trend estimates usually become negligible. Revisions to seasonally adjusted estimates may be noticeable up to three years later, with the number of revisions required being dependent on the time series. Revisions to original estimates are rare.
It is important to note that the ABS revises estimates so that the most accurate possible estimates, at a point in time, are released.
For more information, refer to Time Series Analysis Frequently Asked Questions, 2003 (cat. no. 1346.0.55.002) Issues with Seasonal Adjustment.
The ABS produces a number of publications to assist in understanding and analysing time series. For further information refer to:
For more information on Retail Trade data, refer to Retail Trade Australia, Dec 2010 (cat. no. 8501.0).
For more information on Building Approvals data, refer to Building Approvals, Australia, Dec 2010 (cat. no. 8731.0).
1 Australian Bureau of Statistics, September 2010, Livestock Products, Australia, cat. no. 7215.0, viewed 2 February 2011, <http://www.abs.gov.au/ausstats/abs@.nsf/mf/7215.0> <back