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Thursday, February 26, 2015

tis the season -- or this year, not -- but keep it out of our data

As yet more snow falls, we're reminded ... that it's the start of spring? While this year is colder than any I remember, though not so bad in terms of total snow, it does raise the question of how to interpret economic data. Of course housing starts are down, but they're always down this time of year. Some prices are up and others down, again as in the past. Since it was the most recently updated series -- the new data were released at 8:30 am this morning -- I use the Consumer Price Index as an example.

The graph on the left is of the raw CPI "headline" series, unadjusted for seasonality. As you can see there are regular spikes, up and down, in the data. If you look at the unadjusted series, you'll find that there is a downward spike every November, and an upward spike that includes March. (Click to open it in the FRED database, if you hover your cursor over the graph you'll see the date and value for each point.) If we're the Federal Reserve, trying to gauge what is happening to inflation, we thus know the March number will give a number that is too high, the November one too low. Now we can look at changes from the year before, but that is less than perfect because random factors -- unseasonal weather, Easter falling in March rather than April -- might make price changes in one month higher or lower than normal. We could do a regression to get a monthly adjustment factor, but that implicitly assumes a constant pattern across a span of a dozen or more years.

Work by economists in statistical agencies around the world points to using deviations from a rolling average as superior to a regression. (In fact the methodology was initially implemented in Canada, not in the US.) Formally this is an ARIMA correction [AutoRegressive Integrated Moving Average], which in the software iteration currently used across the government allows correcting for anticipated idiosyncratic factors such as alternate dates for major holidays, e.g., a New Years that falls in the middle of a week or an Easter that falls in April and so shifts the timing of the Spring Break found in many school schedules.

The result is a seasonally adjusted series; I have that for the CPI just below the unadjusted one. It's not a totally smooth series, because the underlying data aren't smooth, but the upward spike in March is muted or absent, and the downward November spike vanishes. The real test comes from looking backward: the consensus of the users of the data is that the correction is pretty good, and that large deviations are generally a function of one-time events that all know will affect the data, but for which there's no historical precedent to make a correction. (An example is the impact of this winter's series of blizzards in the Northeast or the Federal shutdown of a few years ago on employment data – we know there will be one, but it's hard to know the magnitude.)

Now seasonal corrections are not for everyone. If you're trying to do a short-term budget, you want to know the actual price change this year, not whether it is higher or lower than in recent months or relative to a "normal" year. For most purposes, however, we do want seasonal corrections.

For more detail see the relevant BLS page.