I know many of you have been waiting for this and here it is!
New versions of X-13-ARIMA-SEATS have just been released by the United States Bureau of the Census. Check them all out in the following links.
The Bureau of the Census also has a lot of good seasonal adjustment resource information to check out.
We have been very busy here and unfortunately there has not been an opportunity to post any updates. Better late than never… we wish you a productive 2013.
I hope you are not SAD and have seasonal adjustment disorder.
Today the Greek retail sales were released and it made some headlines with
The actual data can be obtained from the ELSTAT website although it doesn’t seem that the seasonally adjusted estimates are made available. This probably explains why the news reports focused on the 12.1% fall between September 2011 and September 2012. But having downloaded the original data we can apply seasonal adjustment (and also calculate trend estimates) by using X-13-ARIMA and see if this changes the interpretation of the most recent data. Plotting this shows…
Some interesting observations.The year-on-year change in September is -12.1% in the original data for September (as reported), but once seasonality is taken into account (e.g. in this case the changing seasonality over the years), this is -11.9% over the year. Calcuating a trend estimate gives the underlying change over the last year of -10.4%.
Having derived the seasonally adjusted and trend estimates this can give us a better indication of what is happening at the current end of the series. While the month-on-month trend changes are still decreasing in the recent six months, the latest data shows a -1.1% change in the trend between August and September 2012. This is a much better indicator of what is going on now than looking at the year-on-year change in the unadjusted data.
Interesting, the plot also shows that the December seasonality is reducing quickly over the last few years. This is more easily seen by looking at the seasonal plot for December below. I have also included August and September data. Some of the downwards monthly movement that is seen for September 2012 can be attributed to the higher than normal August estimates, as the September 2012 data came in pretty much inline with historical September estimates. So perhaps the recent Retail activity is starting to level out.
A relatively obscure journal (well obscure in the sense that it is not main stream and if you weren’t aware of its existence you might not know about it) has put out a set of articles on seasonal adjustment for a special edition.
The journal is the Taiwan Economic Forecast and Policy, and it is Volume 43, No.1 (October 2012). You can access it here: http://www.econ.sinica.edu.tw/academia-02.php. Not all papers seem available for download but you can get access to a few of them.
Some of the papers have been presented at the 2010 Macroeconometric Modelling Workshop on Seasonal Adjustment Methods held during December 9–10, 2010 at the Institute of Economics, Academia Sinica, in Taiwan.
As we’ve mentioned previously, different indicators such as month-on-month, or year-on-year, can provide mis-leading interpretation in times of economic change. One of the papers – (update: which is now available for download) – is by leading seasonal adjustment experts Benoıt Quenneville (Canada) and David Findley (USA). They look at when a time series being measured contracts sharply for a few months and then starts to recover, and how the publication of both the annual and monthly growth rates can give conflicting signals. They show the commonsense fact that in this case the year-on-year ago comparison has a phase shift of around six months and that the month-on-month comparison has a phase shift of half a month. In practice, the use of indicators like this introduce phase shifts in the derived indicators which can delay the detecting of turning points and then lead to mis-interpreting the direction of the series. So basically, year-on-year changes is a bad thing. Memorise this.
I had previously looked at public sector net borrowing in some earlier posts. The most recent data for October was released on 21 November 2012. It again led to quite a bit of press, for example,
The Guardian also has a focus with some analysis, but only presents the annual data in a nice looking graph linking it all back to political parties. See this link.
We can do better than this and use the monthly data and also combine this with some seasonal adjustment techniques to tell us really what is going on. Annual data won’t tell us the true story. The monthly data is available from this link (series id: J5II). The data goes from January 1993 up to October 2012.
So lets first look at what a reasonable expectation should have been for October 2012 estimates. Ideally, we should use the data that was available at September 2012 estimates. This is because there may have been some historical revisions. But unfortunately the ONS website does not make it easy to extract data vintages of previously published data. To make this as realistic as possible I have updated the data based on the published estimates in their previous statistical release. So taking the actual data published up to September 2012 and applying some simple forecasting methods would have given a forecast for net borrowing for October 2012 of around £6 billion. So in-line with the expert economists who probably also just applied a simple forecast model. But this forecast came with a range between £-9.5 billion and £-2.5 billion. A wide range. So we shouldn’t be too surprised that the actual number was £-8.6 billion, as it is well within the expect range of our forecast.
Using the actual published data for October 2012 we can look at the seasonality for October over recent years. This can give us an indication of whether the October 2012 estimate is different to previous Octobers in different years. As everyone knows it is not a good thing to just compare the non-seasonally adjusted data across years as it does not take into account aspects such as changing seasonality over time and calendar composition of the month. The use of seasonal adjustment will account for this. The plot for the seasonal component in both Septembers and Octobers since 1993 is:
This shows a few things. While we didn’t look at the September 2012 estimate in detail, it highlights that this came in as we would have expected based on historical Septembers. For October 2012, this shows that the net borrowing came in actually lower than we would expect by about £2.5 billion, and broadly in line with what occurred in October 2009. So not a good October 2012 result.
This is better illustrated with the seasonally adjusted and trend data. It looks like this:
The black line is the original data (e.g. the £-8.6 billion for October 2012) along with the seasonally adjusted in red, and the trend in blue. Now it becomes clear on the benefits of seasonal adjustment, which strips out the regular seasonal pattern that is observed over the history of the series. Based on historical data we would’ve expected the black line for October 2012 to be slightly higher (e.g. less negative by coming in around £-6 billion rather than £-8.6 billion). This is illustrated more clearly by the dip in the seasonally adjusted movement between September and October 2012. More interestingly, the underlying trend of net borrowing has leveled out since October 2011 with a change in underlying trend of “only” 70 million over 12 months, e.g. essentially unchanged underlying net borrowing for over a year.
And even more finally. For November 2012 estimate, we will throw out a forecast for net borrowing (non-seasonally adjusted) of £+2 billion. Anything less than this and the underlying trend will be going the wrong direction. Lets wait and watch the hype.
The article below is worth a read. It is not often you see these type of nitty gritty statistical issues reported in the mainstream media but it highlights an important issue for compiling and comparing estimates.
While it also seems to be a side promotion for the authors book (which is always the case I guess) it also captures the issue of data quality both within and across different countries.
Compiling statistics such as GDP (in the National Accounts) is not a simple thing. In a lot of major economies there are teams and teams of highly qualified people putting these estimates together. You don’t see them but they are often hidden away in the back rooms of statistical agencies. These brave men and women of the statistical world – yes! don’t laugh! – are often classified as nerds and geeks because it can take an unhealthy obsession with the finer details of the data and nuances of source data to compile a high estimate of GDP. It is often the case that with such a complex area, individuals will have over 20 or 30 years of experience in specific aspects of what makes GDP tick. It is not an easy task. And it is often why they are locked away in the back rooms.
A quick aside – and lately it seems to be a thankless task as the debate about the usefulness of GDP versus well-being measures rumbles onwards. Maybe this will be a topic for another post…
In this example, the compilation of GDP estimates is a worthwhile exercise, but what it really shows is the importance of getting the fundamental basics of the estimates correct. It also shows how vital it is to have regular revisions to country estimates, particularly when new or updated historical data becomes available, such as the contribution of different sectors of the economy. There are many detailed international manuals and frameworks for GDP compilation which have been around for many decades and are updated on a reasonably regular basis. The issues described in the article above are captured in detail in these types of manuals.
The manuals cover a lot of detailed points but if the basics such as having some fundamental knowledge and understanding of key concepts, while also having access to timely and quality source data, aren’t in place then in the end it doesn’t matter what the manuals (or consultants, or booksellers) actually say.
The UK unemployment estimates were released today for data including the September period. Previously, I’d put my non-existent reputation on the line and went with a prediction that the unemployment would go back up in September.
Well. I’ll hold my hand up here and admit that I was wrong on the magnitude on this one. For the monthly estimate I was correct in predicting an increase (see below), but I was quite a bit off in the magnitude. Although the makings of a good forecaster is to make lots of forecasts and eventually you’ll be right more times that you’re wrong. Or even just make too many that no-one can keep track of them all. In this case I’d written in stone that the headline rate for July to September 2012 would be around 8.1%. It came in at 7.8%. So a good number in the context of the wider economy but quite a bit under the estimate.
To dig a bit deeper I’ll use the monthly estimates that were published today to try and get a better understanding of the previous forecast. Plotting the experimental monthly estimates for the UK 16+ unemployment rate, with a calculated Henderson trend estimate gives
Here we can see that on a monthly basis the seasonally adjusted unemployment rate for UK 16+ went from 7.6% up to 7.7% in September. So even though it was up slightly, it was not up by the amount I had thought. I had given a range of 8.0% to 8.2%. In any case, this does not have a significant impact on the previously calculated trend estimate, so the trend is still robust in this example.
So what went wrong? Well, any model is only as good as the underlying assumptions. Based purely on the data up to August estimate and a correction for a possible one-off Olympic effect, in my earlier post I said I’d settle for an estimate between 8.0 and 8.2%. The actual confidence interval based on data up to August 2012 and no correction for the Olympics was a forecast for September of 7.3% to 8.2%. Which is very wide. If I’d stuck to the confidence intervals of this forecast that I’d have ticked the box but it would have not been much use as the range is so wide.
The problem in this case is due to at least two things. I have used the aggregate data, and based the simple ARIMA forecasts on these aggregate estimates for the rates. Given the complexity of the labour market, a more appropriate forecast would use separate forecasts for the numerator and denominator, and also at lower level aggregates. Then constructing an aggregate forecast. This would take into account aspects that are happening at a sub-component level such as the impact of Olympics only on particular sectors or geographical areas. The previous forecast also used an assumption on the impact of the Olympics, where there was a presumption that it had distorted the August 2012 estimate and was a one off impact. Now this assumption could have been wrong, e.g. there is a lasting effect of the Olympic employment, or the magnitude that was adjusted for was taking too little off the estimate used for the forecast.
So putting this all behind us and looking forward… what can we say about an expected forecast for October 2012? Taking the monthly aggregate data again at face value gives a forecast range of 7.4% to 8.3%, with a predicted value of 7.9% for a monthly UK 16+ estimate for October 2012. Again, the range is very large which is not very useful if we want to anticipate a fall or rise. In any case, a monthly value of 7.9% for October is equivalent to a headline quarterly rate for August to October 2012 of 7.7%. So a slight fall from the current 7.8%. This is a good example of where taking a simple 3-monthly average (e.g. which is essentially what the published quarterly estimate is) is not the best thing to do. As even though there could be a rise in monthly unemployment in month of October, there will be a fall in the quarterly rate because the value for July 2012 of 8.2% drops out of the calculation. This is something to look at closely next month.
The very good thing about forecasting and assumptions is that we rarely know the truth (until either the next data point comes in, or the data is revised very far in the future when everyone forgets the forecast). So in the end I will have to eat humble pie on this occasion.. but there is always next month to be wrong again.