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.”

Proposal: “Easter to be fixed to one date all the time”

Concerning news for all fans of seasonal adjustment around the world, particularly on the treatment of Easter!

If this goes ahead at least there will be some work in updating all of the seasonal adjustment packages, estimating and applying seasonal pattern breaks, and making consistent long run time series!

“The Most Rev Justin Welby said that he hopes to make the change within the next five to ten years, in a move that will likely have huge knock-on effects for schools and other seasonally-dependent industries, according to reports.”

Although they have a history of taking their time!

“Mr Welby did warn however that churches have been attempting since the tenth century to fix the date of the festival, which at the moment is set with reference to the moon and the sun.”

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: