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Seasonal adjustment in Stats NZ
How to interpret output from seasonal decomposition

What do we use the actual (observed), seasonally adjusted, and trend series for?

Use the actual series to look at the current quarterly or monthly level.

The actual series will give you an idea of what happened that particular month or quarter.

The problem with using the actual is that it is influenced by seasonal effects (Actual = Trend * Seasonal * Irregular). These seasonal effects may be masking the true movements. For example, in electronic card transactions, December is a very high month due to Christmas sales. If we compare November to December sales, we would report an increase in sales. But this increase is largely due to seasonal fluctuations and is not an informative measure.

Use the seasonally adjusted series to compare short-term movements (monthly or quarterly) between series.

The movement is attributable to changes in the irregular component and changes in the trend.

If the movement of a set of seasonally adjusted series were similar then it would suggest that there is a common underlying cause which is independent of any individual series.

If the movement of a member of a set of seasonally adjusted series were markedly different from the majority of the others, then it would suggest that there is a cause peculiar to that series which is worthy of investigation.

Use the seasonally adjusted series to compare different periods of the same series.

Because the seasonal component has been removed from the whole series, we can uncover interesting movements in the series.

The graph below shows the food retail sales series from November 1998 to August 2000. The December peaks are clearly visible in the actual sales. The seasonally adjusted "peak" for December 1999 shows that pre-millennial food sales were greater than would have been expected for an ordinary December month. The fact that the January 2000 seasonally adjusted food sales is almost coincident with the trend suggests that the food stocked up in December was not detrimental to the January sales.

Graph, Food Retail.

Use the trend to look at long-term movements of individual series. The trend shows the relatively long-term movements underlying the time series. Changes in the prevailing conditions are expected to be reflected by changes in the trend movement.

When making interpretations of the trend, the user must be aware that the choice of trend estimator will affect the movements that are retained. A moving average estimator tends to suppress all effects with a duration shorter than the span of the moving average. Therefore the longer the span of the moving average, the smoother the trend is, and the less detail on local features of the data retained.

Statistics New Zealand trend estimates have the advantage of being objectively selected, able to be replicated, and using an internationally accepted methodology. Most of the effects of less than 12 months duration have been removed.

The trend is useful for indicating turning points in the underlying series. But there is an uncertainty attached to the trend direction for the most recent points. This is because of revisions to trend estimates in the most recent quarters (Why do trends get revised?) The months of cyclical dominance (mcd) or quarters of cyclical dominance (qcd) give an indication of the uncertainty.

For example, the total (monthly) electronic card transactions trend has mcd=2. This indicates that it takes about two months of subsequent data to confirm a turning point.

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Why is it possible for the movements in the seasonally adjusted series to be in the opposite direction to the year-on-year movement of the actual series?

The movement of the seasonally adjusted figure gives the movement of the trend and irregular component from the previous month/quarter. The year-on-year movement of the actuals gives the movement of the trend and irregular component from one year ago, assuming that there is negligible change in the seasonal component.

We would expect the two changes in the irregular component to be of comparable size, but not necessarily in the same direction. We would not expect the two changes in the trend to be of comparable size, and, especially in the vicinity of turning points, they may not be in the same direction.

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Which is the best measure of movement: year-on-year or month-on-month (quarter-on-quarter)?

Comparisons to the same period in a previous year (whether they are monthly, quarterly or annual) are particularly poor in identifying turning points in time series measuring the economic performance of an industry. On average there will be a lag of six months in the identification of a turning point when using this type of analysis.

In his monograph "Electronic Computers and Business Indicators"(1), Julius Shiskin writes the following:

"The simple device of same-month-year-ago comparisons is frequently used to eliminate seasonal fluctuations. Same-month-year-ago comparisons involve dividing the figure for a given month by the figure for the same month of the preceding year. This practice is widespread among financial writers and businessmen and is occasionally followed by professional economists and statisticians."

"The simplicity of the same-month-year-ago comparisons is, unfortunately, offset by major drawbacks. These drawbacks are sometimes critical at cyclical turning points. When a cyclical decline occurs, it usually takes a continuation of the tendency for several months before a decline below the same month of the year before becomes apparent. In using raw data for current analysis, same-month-year-ago comparisons tell broadly what has happened over the intervening twelve months, but not during that period. Such comparisons often will not indicate correctly the trend during the preceding six months, which is crucial in most current business analysis."

(1) Shiskin, J 1957, "Electronic Computers and Business Indicators", National Bureau of Economic Research Inc., Occasional Paper 57, pp 225 and 228, Cambridge, Mass.

The quarter-on-quarter movement of the seasonally adjusted series is less prone to revisions, and therefore is often used for commentary. But, as illustrated in the example of the department stores above, it is not informative in the vicinity of turning points.

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Why don't the seasonally adjusted figures sum to the annual actual figures?

For a multiplicative model, when the seasonal factors are calculated in X-13-ARIMA-SEATS, they are renormalised to sum to 1 across each year. This ensures the annual sum of the seasonally adjusted series is approximately equal to that of the actual series. They are not exactly equal because of incomplete cycles, outlier treatment, etc.

Statistics New Zealand does not use the benchmarking X-13-ARIMA-SEATS option that forces the adjusted series to have the exactly the same totals as the unadjusted series.

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Can I get seasonally adjusted annual data?

Seasonal adjustment adjusts for patterns that occur within a year. Annual data is not affected by this sub-annual pattern, so the concept of seasonally adjusting annual data is meaningless.

It is possible to produce a trend for a series of annual data. This can be done by a applying a weighted moving average.

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Do monthly seasonal adjustments sum to quarterlies?

No. Statistics New Zealand adjusts quarterly data independently of the monthly adjustment. The monthly actual figures are summed and then seasonally adjusted. This gives slightly different results to summing the seasonally adjusted monthlies. (For the theory see "Analysis of the difference between the quarterly seasonally adjusted series and the summed monthly seasonally adjusted series").

For more details see the downloadable file: "Analysis of the difference between the quarterly seasonally adjusted series and the summed monthly seasonally adjusted series"

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