It’s a leap year

“Assessing the economic impact of a leap year is tricky. In the UK, the Office for National Statistics adjusts GDP to make all Februaries comparable, so February is considered to be 28 and a quarter days long every year, regardless of whether it’s a leap year or not.”

Chinese GDP calculation and seasonality

Always interesting to read how different countries calculate their economic outputs, particularly GDP. This recent news article covers some changes to the Chinese GDP calculations with aspects relating to seasonality.

The relevant bits are:

“Now, China is calculating GDP based on economic activity of each quarter to make the data “more accurate in measuring the seasonal economic activity and more sensitive in capturing information on short-term fluctuations”, the NBS said.

Previously, China’s quarterly GDP data, in terms of value and growth rates, was derived from cumulated figures rather than economic activity of that particular quarter, the bureau said.”

Always good to go back to the original source which seems to be at:

in the sections

“1.4.1 Preliminary Accounting

As China’s quarterly GDP accounting is cumulative before 2015, the GDP preliminary accounting of 1-4 quarters is annual GDP preliminary accounting. Since the third quarter of 2015, China’s quarterly GDP accounting is completed quarterly, which means calculating the GDP of four quarters respectively, and totaling them up to produce the annual GDP preliminary accounting results. Annual GDP preliminary accounting is accomplished before 20 January. “

Would be curious to see some time series analysis of the outputs, or how they may deal with any changes in seasonality at this switch over.

UK Bank Holidays and Retail Sales

Unofficial estimates of retail sales for August 2015 from the British Retail Consortium are mentioned in this article: from 8th September 2015.

This time period included particular issues which are relevant to seasonal adjustment, such as the treatment of the bank holiday which fell on 31st August. The article notes that:

“The bank holiday was on 31 August, but both the BRC and the Office for National Statistics judge that the month officially ended on 29 August. It means September’s figures will be boosted by back-to-school purchases. The bank holiday applied in England, Wales and Northern Ireland. Retailers report their sales on a weekly basis from Sunday to Saturday, which means that monthly figures do not necessarily cover the whole of a calendar month. Instead, a quarter will be made up of two four-week periods and a five week period. This is only particularly important when key shopping days such as bank holidays officially fall in different months from year to year, which makes comparisons difficult.”

The article doesn’t mention that if the seasonally adjusted estimates are used, then this problem is not relevant. Any comparison of the collected data which is not seasonally adjusted will be distorted by these type of events, but the use of seasonal adjustment approaches can estimate and remove the impacts of holidays, including those holidays that move over time. So only use the seasonally adjusted estimates to get the real underlying picture of what is happening. Even better is to use trend estimates that can be derived by smoothing the volatility from the seasonally adjusted estimates. So it is best to wait for the official seasonally adjusted estimates to see the real picture.

Residual seasonality and GDP in the USA

Good to see the Bureau of Economic Analysis being so transparent in the link below. Residual seasonality is the ultimate seasonal adjustment bogey man. So it is important that any seasonally adjusted estimates, especially something as high profile as GDP, are assessed for residual seasonality. Basically, if a seasonally adjusted series is still seasonal, then the job hasn’t been done properly and there is some systematic calendar related variation still hanging around.

This typically occurs when aggregate estimates are derived from more detailed seasonally adjusted estimates, and then small amounts of “seasonality” can add up. It also occurs when the seasonal adjustment approach has not been applied in an optimal way.

The full BEA briefing note from May 2015 notes that:

“Each spring, BEA conducts an extensive review–receiving updated seasonally adjusted data from the agencies that supply us with data used in our calculation of GDP. Most of the data the feeds into GDP is seasonally adjusted by the source agency, not BEA. At the same time, BEA examines its own seasonal factors for those series that BEA seasonally adjusts itself.”

Full article here:

So, given that a lot of the estimates are supplied to BEA, it has to hope that these inputs are top notch or there could be issues. At least with some form of a residual seasonality test, they would be able to pick these issues up.

One way to check for residual seasonality is to seasonally adjust the seasonally adjusted output. The premise being that this will identify any additional seasonality as it is treating the seasonally adjusted estimates as the non-seasonal series. This approach does have its own problems depending on which seasonal adjustment approach is used, as a double application of seasonal adjustment methods can not be as powerful in its detection of the seasonal cycles that it has already removed. The HEGY approach for testing for unit roots is a good one to use for checking for residual seasonality (link:


Choose the right indicator for analysis

I normally post articles that are useful to read. The author of the following article does themselves no favours with a general rant against official statistics outputs. I’ll quote two parts of the article that deserve to be highlighted:

The full article is available here:

With the first quote of:

“… comprehensive compilation of data is useful for economists and analysts, it is broadly unhelpful for anyone who wants to get a simple understanding of the direction of retail.”

I’d argue that nothing is simple anymore when it comes to interpreting movements in economic data. Simple analysis will lead to simple understanding and when it comes to the complex nature of economic outputs and estimates you are going to miss the subtle underlying aspects of the economic picture. Why constrain your analysis to simple measures and one indicator? The best approach is to build a picture of a set of outputs and look at a range of indicators. Seasonally adjusted and trend estimates can help give a useful picture when used in tandem; including even looking at the unadjusted estimates if needed. Just focusing on a single indicator is a recipe for disaster for interpretation and understanding as each indicator has its own strength and weakness.

The second quote from the article backs this up. The quote is:

“The more sensible measure is to look at the value of spend compared to the same period last year.”

Unfortunately this is a common misconception but ends up resulting in flawed analysis. It shows a lack of understanding of time series analysis issues in general. Firstly, depending on what data is being compared, year-on-year movements in non-seasonally adjusted estimates run the risk of resulting in seriously misleading analysis. This is because the nature of the calendar changes over time. July this year in 2015 has a different number of day composition compared to July last year. July 2015 has 4 weeks and an extra Wednesday, Thursday and Friday; while July 2014 has 4 weeks and an extra Tuesday, Wednesday and Thursday. So if there is lots of extra activity on a Friday, the results of this comparison will be disorted just by how the calendar changes over time. You may think that you are comparing like-for-like when you look at year-on-year movements, but if the data is not seasonally adjusted (including for trading day aspects such as the number of Mondays, Tuesday etc.) then you will get a false understanding of the movements resulting in changes that look important and significant but are just due to the calendar change. So it is important to ensure that seasonally adjusted estimates are used for any year-on-year comparison. Secondly, a year-on-year movement is lagged and tells you nothing about what is happening in the most recent periods. It only tells you what was happening against a year ago! How is that relevant when you’re ignoring the most recent set of information, e.g. May, June, July outputs in any analysis? The economy evolves over time, and a year ago can be a long time in the context of economic activity. Seasonal patterns change over time, and there can be shocks to the economy. To truly understand what is happening now, the most recent time periods need to be considered and taken into account in comparison with the latest data. The best way to do that is to use a form of trend estimates over the most recent time periods.

A response article that touched on these issues raised by the original article was also published and is available here:

Useful guidance on communicating uncertainty

The Government Statistical Service in the United Kingdom have put out some useful guidance on communicating uncertainty. You can check it out here:

The most interesting part on page 4 is they say

“You should provide sufficient and appropriate information to indicate:
…a longer term view of change (e.g. trend)”

Good to see the trend get an official mention as when it is packaged with a range of other indicators (original and seasonally adjusted estimates), it can give a complete understanding of the nature of the time series. Why settle just for the seasonally adjusted estimates when it still contains the noisy part of the time series?

Seasonally adjusting Greek retail sales

Today the Greek retail sales were released and it made some headlines with

“…evidence that Greece’s economy is still contracting – Greek retail sales tumbled by 12.1% in September, compared with the previous year. That follows a 9.3% decline in August, showing that the slump actually picked up pace.”

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…

Greek retail sales to September 2012

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.Greek retail sales seasonal and irregular chart