The ABS went on to say, "As there is little evidence of seasonality in the July, August and September months for 2014, the ABS has decided that for these months the seasonal factors will be set to one (reflecting no seasonality). This means the seasonally adjusted estimates (other than for the aggregate monthly hours worked series) for these months will be the same as the original series and this will result in revisions to the previously published July and August seasonally adjusted estimates."

I have enormous respect for the ABS, so I am not going to speculate on whether it got this call right or wrong. What I would like to know is what this decision means. And to do that, we will look at the national unemployment rate statistics for persons.

First, however, a quick recap on the seasonal adjustment process. With the monthly labour-force series, ABS uses a multiplicative model of seasonal adjustment, which is described here. The key formulas are as follows:

Original(t) = Trend(t) * Seasonal(t) * Irregular(t)

SeasonallyAdjusted(t) = Original(t) / Seasonal(t)

With a little algebra from the above formulas, we can see the seasonal factor the ABS has applied (including the 1.0 for July, August and September 2014) in the next chart, which plots in blue the seasonal factor applied for each month from February 1978 to September 2014. The red horizontal line is the mean seasonal factor for each month. This chart is evidence that seasonal factors can and do change over time (have a look at December).

To have a look at what the ABS decision meant, I am going to apply the seasonal factor from 2013 for July to September to the 2014 calculation (as an approximation). The values I am substituting back are: 0.937385, 0.975908 and 0.991445.

Because the three relevant seasonal factors are all less than one, their effect is to increase the seasonally adjusted unemployment rate for the impacted months - particularly for July (which spiked at 6.4 per cent).

The ABS uses a 13-term Henderson moving average to derive the trend from the seasonally adjusted series. The resulting trend with seasonal adjustment applied for the past three months is now noticeably higher than if it were not applied. If the July result is a rogue, I would expect this difference to decline over the next four months, as further data points emerge.

For me the really interesting question is what will the ABS do next month. If you look at the first chart above, October and November are both months where the seasonal factor boosts the raw unemployment rate to yield a higher seasonally adjusted rate.

**Update**

Another way to think about this problem is to apply my own seasonal adjustment to the original data. Unfortunately, I do not have as sophisticated software tools as those used by the ABS. I cannot make seasonal adjustments for moving holidays (such as Easter). Nor do I extend the the original data series using a seasonal, auto-regressive, integrated, moving average (SARIMA) regression forecast before undertaking the seasonal decomposition. Consequently, my seasonal weights and final results differ slightly from the ABS. Nonetheless, the results I obtain are reasonably close to the above analysis.