The United States reported their Retail trade statistics the other day (July 16 2012). And quite rightly this picked up a bit of press where it was reported that they fell for the third month in a row. As is usually the case, these falls refer to changes in the seasonally adjusted estimates. And three falls in a row is starting to look like something bad for all those retailers (and perhaps the wider economy).

But given that the seasonally adjusted estimates still, **by definition**, contain a degree of volatility and also an underlying trend, we can go one better and derive our own smoothed estimate of the seasonally adjusted estimates. This will help us cut through the volatility and check out the underlying direction of the data.

We derived a trend estimate in the following way.

- Downloaded the data from here: http://www.census.gov/retail/marts/www/timeseries.html
- Plugged them into R (statistical package)
- Applied a 13 term Henderson filter to the full seasonally adjusted data to generate a trend estimate
- Used the ggplot2 package in R, which produces very nice plots (but can take some effort to get the data into the right format, e.g. a dataframe with all the right bits)
- And we get the following picture with a trend line…

I’ll leave the interpretation to the so called experts but it could be that with these three falls in a row in the seasonally adjusted estimates, retail activity in the US has started to reach a turning point. But. And this is the big but. We’ll need more data to make sure. This is because it is difficult to understand if what we are seeing is due to random variation or a change in direction of the underlying trend.

Just for completeness, the following table gives the one month percentage change in the different estimates. You can see that the one month change in the seasonally adjusted estimates can jump around, but the one month change in the trend is cutting through this noise and indicating a possible turning point.

Nov 2011 | Dec 2011 | Jan 2012 | Feb 2012 | Mar 2012 | Apr 2012 | May 2012 | Jun 2012 | |

Trend | 0.66 | 0.63 | 0.50 | 0.33 | 0.19 | 0.08 | -0.01 | -0.07 |

Seasonally adjusted | 0.47 | 0.04 | 0.64 | 1.03 | 0.37 | -0.51 | -0.17 | -0.48 |

Other approaches could of course be used with different filters being applied and these would give slightly different results depending on the type and length of the filter used. It would have also been more useful if there was an official estimate of the trend as it would’ve saved some time as this is can be produced as a by-product of the seasonal adjustment process. One good thing about the data that can be downloaded from the census site is the availability of the seasonal factors, and also the sampling variability of the estimates. This is something you don’t often see being produced. So this is a big plus to have.

Also note that there are a few different estimates floating around in the dataset, particularly: advance estimates, preliminary estimates, revised estimates, and then suppressed and also not available. So this can potentially be a bit confusing as each of these estimates will have different characteristics. This is something to keep in mind if you’re grabbing the latest information from any data source is that it can often be revised as new data becomes available. Actually – this is really a good thing as it means that we at least have the best, latest and most up-to-date information.

I see your support for National statistics agencies to publish trend data. I am aware this tends to be a controversial issue, particularly between statistician and economists. For their nature, economists like to do predictions – as you well observe in one of your other posts. I suspect that if trends were officially published it will be all too easy for economists to use them as predictive/forecasting models, which it would be clearly misleading. So i can understand the reluctance to routinely publish trend figures.

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