X-12-ARIMA

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.

Light Dawns on Marble Head

A friend of ours was fond of using the expression, "light dawns on marble head" as he slowly perceived what he believed to be obvious and right there before him had he only been more attentive.  So it may be with all of us, from time to time.  Sometimes things are not at all obvious, though, and we're simply being modest, as was the case with our friend. Sometimes it's simply a matter of jotting things down that can be viewed in plain sight.

Plotted below is the yield on the 30-year UST at roughly its high and low marks for the year, for each of the past four years (2010-2013).  The cyclical high yield in each year has come in the rather narrow period of late March – early April.  In fact, the high yield has printed in a period spanning no more than 26 days!  US Treasury bonds, particularly at the long end of the yield curve show their greatest price reaction to economic strength or weakness, signs that their greatest foe, inflation, might be creeping in or receding.  Hence, when the economy appears to be at its strongest, the 30-year trades its weakest and prints its high yield for the cycle.

The cyclical low in yield for the 30-year has occurred in a somewhat wider range over the past three years, from late July – early Sept (too early to tell for 2013).  While this is a wider period than its high yield mark, this data still indicates a span of less than 45 days.  Now, perhaps this is purely coincidental that the 30-year would signal its greatest price strength and weakness at precisely the same time each of the past four years.  Or perhaps, there's some pattern worth discerning.

Why this pattern might occur requires some speculation, but as another friend of ours was fond of saying, "numbers don't lie".  We believe the reason for this trend is the economic false-starts we’ve seen for Q1 for the each of the past three years and, we suspect, carrying over into Q1 2013.  As discussed in  a previous post on this blog, the data from BLS and Commerce have been favorable in each winter period for the past four years, causing bond prices to weaken, only to fall off in spring and summer (causing bond prices to rally).  

We believe that this pattern is not coincidental, but rather relates to the seasonal adjustment models that the two departments use to account for what they believe to be normal seasonal patterns. If true, these factors are distorting the picture of growth in the winter months, causing the UST long bond to weaken substantially (in price) only to recover strongly as that growth fails to carry forward into the warmer months. 

The best description of the seasonal adjustment factors we've seen was in a blog post to the Washington Post:  http://www.washingtonpost.com/blogs/wonkblog/wp/2012/08/05/wait-the-u-s-economy-actually-lost-1-2-million-jobs-in-july/