USA retail sales and trend estimates for August 2015

It has been a long time since we’ve looked at the USA Retail Sales estimates. Way back in 2012: so it is worth a revisit.

The Census Bureau do not estimate or publish official trend estimates, but trend estimates can be derived by taking the published seasonally adjusted estimates and applying a set of Henderson filters (with a bit of code in R and ggplot2). Using the latest published data up to and including August 2015 gives

USA Retail Sales Seasonally adjusted and trend estimates

where the one month percentage change in the trend and seasonally adjusted estimates are

Dec 2014 Jan 2015 Feb 2015 Mar 2015 Apr 2015 May 2015 Jun 2015 Jul 2015 Aug 2015
Trend -0.24 -0.18 -0.01 0.26 0.49 0.58 0.53 0.45 0.36
Seasonally adjusted -0.87 -0.77 -0.53 1.54 0.03 1.18 -0.04 0.71 0.19

So underlying one month movement in the trend has been strong since March 2015 even though the seasonally adjusted one month movements have bounced around. Even with a dip in the seasonally adjusted estimate in September 2015, it shouldn’t change the fundamental view of the underlying strengh in recent periods.

Over the length of the series the median for the one month percentage change in the trend for USA retail sales is 0.4%, so the recent activity is back in line with historical growth.

For background you can get the seasonally adjusted data here:

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:


Excellent resource for seasonal adjustment related articles

For those in the know, the United States Census Bureau website is a good resource for technical seasonal adjustment papers.

Good to see legends of the field in David Findley and Agustin Maravall still getting their expertise and knowledge out there.


“lluminating Model-Based Seasonal Adjustment with the First Order Seasonal Autoregressive and Airline Models, by David F. Findley, Demetra P. Lytras, and Agustin Maravall (CSRM Research Report, 2015”

Wavelet benchmarking

Wavelets are the way forward. It will be interesting to eventually see a wavelet approach to seasonal adjustment, but in the mean time, here is some research work for the use of wavelets to benchmark time series. The title is “An Introduction to Applications of Wavelet Benchmarking with Seasonal Adjustment”.

The full article is available here:

In it they note that: “The versatility of the procedure is demonstrated using simulation studies where we provide evidence showing it substantially outperforms currently used methods. Finally, we apply this novel method of wavelet benchmarking to official Office of National Statistics (ONS) data.”

Cutting edge stuff!

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: