Tuesday, April 30, 2013


We've written several posts on the subject of the seasonal adjustment of data from Commerce, BLS and US Census departments.  The beast that crunches the seasonal adjustment modelling for the Census Department is simply known as "X-12-ARIMA".  The raw (unadjusted) data is pumped in and X-12-ARIMA takes care of everything else.

Here's a look at how powerful the seasonal adjustment factors (SA) are with respect to time series data for the unemployment rate.  The blue line is the reported seasonally adjusted data.  The red line is unadjusted. You can see how lumpy the unadjusted data is, lending credence to the argument that the data should be reported SA, in order present a more cogent picture of employment trends, through seasonal periods.

While the smoothing perhaps presents a clearer picture of trend, at the same time the SA data does not reflect at any point in time the true unemployment rate (unless the two curves periodically intersect).   For instance, for January 2013 when the unemployment rate was reported as 7.6%, the actual rate (number of persons reported unemployed/labor force) was approximately 8.5%.  No big deal.  The two trends are moving lower.  But what about other time series data?

The retail sales data on an unadjusted basis shows a similar lumpy pattern (red line).  The pattern here is again smoothed by the seasonal adjustment factors.  But with retail sales, the distortions caused by adjusting data may be more meaningful.  We all know retail sales climb during the holiday season at year end. We also know that sales tend to fall off in January once the bills arrive.

But what is interesting are the portions of the graph below the SA line and above the unadjusted line.  What these gaps represent are periods where the seasonal adjustment overstates true retail sales activity in the economy.  

While the SA factors tend to mute the explosive growth in retail sales during the holiday period at year end, these factors then consistently overstate economic growth during periods of greatest sales declines.  This is equally true with employment, which also peaks in Q4 and troughs in Q2.

As can be seen from the graphs above, the most significant impact of both of these adjustments occurs during the first half of each year (Q1 for retail sales and Q1-Q2 for employment).  Since financial markets trade off the headline numbers for both which, again, overstate activity during Q1-Q2 of each year, this consideration might explain the pattern of the stellar performance of stocks during the first quarter and the consistent "spring swoon" that we've seen for each of the past three years.