Unfortunately the full article below is entrenched behind the paywall of www.thetimes.co.uk. But it is an insightful article by Sam Fleming and the selected extract below is useful to illustrate an important point.
“Wednesday’s numbers undoubtedly overstated the depth of the dive in GDP in the second quarter, in part because the Office for National Statistics struggled to measure the impact of bad weather and the Jubilee holiday. The 0.7 per cent drop is likely to be followed by a bounce of a similar magnitude in the third quarter, thanks to Olympics-related spending. Both quarters’ numbers should be treated as radio static. Britain’s growth is basically flat.”
Read it at: www.thetimes.co.uk: Caught in a Fiscal Ditch, 30 July 2012
This is all interesting stuff and what is really being talked about here are one-off events. The terminology can vary but these are typically referred to as irregular, one-off, special, extreme, or abnormal events. So pick your word of choice. In the end it doesn’t matter what we call it because these type of events are out of our control and we can’t stop them happening. What is more interesting is the interpretation and also the measurement.
Obviously these type of events can have either a positive or negative impact on important economic estimates such as GDP or retail sales. For example, the impact of extreme unseasonal weather could cause retail sales to plunge, (or conversely sales of scarves and winter jackets to soar), or the timing of the Olympics will cause travel and spending patterns to change from what they would normally be. The occurrence of these types of events all pose challenges for users, such as economists, for the interpretation of the outputs but also for the statisticians who use statistical methods like seasonal adjustment. When seasonal adjustment is boiled down to the bare bones it is just the estimation and removal of systematic calendar related effects, and if we get a curve ball of something unexpected then this can cause us some difficulties in applying these methods. However, all is not lost. There are ways that these events can be estimated for and removed to help the interpretation of what we are really interested in.
When these events like this occur what we should be interested in is the underlying direction of the time series. While it is important to estimate the magnitude of these one-off events it is often not possible to do this immediately. Often, before a thorough estimate of the impact of a one-off event can be made, more information is needed such as additional survey data which may take months or even years to arrive, or even waiting for additional anecdotal information from an independent source which can verify the impact. But it is almost never the case that this type of information is available in time to use when deriving the seasonally adjusted estimates. Everyone wants the latest data as soon as possible!
An important point to note is that for the purposes of the seasonal adjustment program, it doesn’t care what the reason was for the one-off event. It even doesn’t care that it happened. Depending on the seasonal adjustment program, it can try to deal with the data in its own automatic way. For example, the commonly used X-12-ARIMA seasonal adjustment package includes an automatic algorithm to correct for data points that it thinks are abnormal. By doing this it helps improve the estimation of the seasonal factor while also generating robust outputs. Leaving that aside for the moment, if we did have additional information, such as the reason for the one-off event, an expected magnitude of impact, or some anecdotal information, we could use this to prior adjust the data ourselves and attempt to fix this before we used seasonal adjustment. This would be the best thing to do as we have more control and it would help the seasonal adjustment program get the best seasonally adjusted set of estimates as possible. Experts do this all the time, particularly at National Statistics Institutes. However, when this is not possible, there is another different way.
We can simply treat any one-off event as being part of the irregular component. Remember that the collected data typically consists of three main components: a trend (underlying direction), seasonality (due to calendar effects, weather etc.), and irregular (volatility due to real world variation, or due to sampling or due to other random things).
This means that our seasonally adjusted estimates still contain the trend and the irregular component (this is not a problem as it is always the case). So following this approach, the trend can now become our friend, as we can reduce the impact of one-off events, and we can calculate a trend estimate in the following way:
1. Take the published seasonally adjusted estimates (which be definition will include all the one-off effects). This can be obtained from the ONS website.
2. Apply a Henderson filter which can reduce the impact of the irregular component, isolating the trend. In this case the Henderson is a 5 term filter, with an I/C (noise to trend ratio) of 2.0. Other options could be used.
Doing this for the UK GDP estimates, up to quarter two 2012, gives the following picture.
So what does this tell us?
So while we now have a trend estimate it doesn’t tell us the exact impact of the one-off event. We could derive an estimate of this by using the seasonally adjusted estimate (which is trend and irregular) and the trend estimate to give us an impact of the irregular. However this does not tell us precisely the impact of the special or one-off event because additional volatility may be within the irregular component.
If we go back to the original quote in the article… “Britain’s growth is basically flat”. Well, perhaps yes or perhaps not really. If we did have additional information on the magnitude of the abnormal events, this would result in a “flatter” trend as the recent time point may be adjusted upwards. Even ignoring the measurement issue for the abnormal event, we can still obtain a trend estimate which helps cut through the volatility of the seasonally adjusted estimates. And the best thing is that rather than use meaningless words we can actually quantify the movement in the trend. The table below best illustrates this. Rather than watching the seasonally adjusted estimates jump all over the place from positive to negative to positive to negative, the trend estimates show a clear change in direction in the recent two quarters.
So go for gold, go for the trend.