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All the explanations of seasonal adjustment that I found from a quick search either don't give any quantitative examples, or give an example with a time series that is either made up or represents an extremely specific microeconomic data set.

I'm curious, what does the seasonal adjustment curve look like for major macroeconomic variables like GDP or the unemployment rate? I don't need precise numerical values; I'm just curious about what the curve looks like visually - what are the busier and slower times of year, and what is the order of magnitude of the deviations from the annual mean.

(I know there are different methods for seasonal adjustment, e.g. additive vs. multiplicative models - either one will do.)

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  • $\begingroup$ Friend, Do you want to see an images or an example using numerical values? When it comes to patterns, it really depends on what country you are looking at and time of year. For example, for the US , GDP's first quarter is usually substantially weaker. $\endgroup$ – Mike J Jun 9 '20 at 2:41
  • $\begingroup$ @MikeJ A plot is fine; I'm just curious about the overall shape and the scale of the relative fluctuations about the annual mean. I'm mostly interested in the US, but I'd be interested in seeing other countries' curves as well. $\endgroup$ – tparker Jun 9 '20 at 3:03
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Quarterly GDP seasonally adjusted enter image description here

source: https://aneconomicsense.org/category/econ-data/gdp-productivity/ AnEconomicSense.org by Frank Lysy

Monthly unemployment rate seasonally adjusted

enter image description here

Source: https://www.researchgate.net/figure/Seasonal-adjustment-of-US-unemployment-using-the-defaults-of-seasonal-The-result-is_fig2_329822239 by Christoph Sax and Dirk Eddelbuettel

These are just some examples.

To manually do it in excel this link from Catherine Hood shows an example

http://www.catherinechhood.net/SeasAdjShortTimeSeriesExcel.pdf

simplest case- – A Quarterly Series with a Flat Trend

Steps to calculate the seasonal adjustment:

  1. Calculate the average for the series. This will be use as the trend.

  2. Calculate the difference between the original series and the trend. Label this as "residual"

  3. Calculate the seasonal factors (SF), which are the average of the residuals for a given quarter.

For example, the seasonal factors for all the Quarter 1 values will be (111+87+145) / 3 = 114.3333 and so on.

  1. Subtract the seasonal factor from the original series to get the seasonally adjusted series. For example, for Quarter 1, 1991, we have 864 – 114.333 = 749.6667.
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  • $\begingroup$ Thanks, this is helpful, but do you have any plots of the seasonal adjustment curve (i.e. the amount that you add to the data or multiply it by in order to remove seasonal fluctuations) over a single year? That's what I was really looking for. $\endgroup$ – tparker Jun 9 '20 at 12:31
  • $\begingroup$ I will check. The different seasonal adjustment programs (X-11 ARIMA , X-12, X-13 ARIMA SEATS) might that information located in the developers website. When it comes to seasonal adjustments there are lots of different options that one can select to perform the modification to the data. It really depends on what your data looks like over time and if there are outliers. Here is an example of one program that census keeps census.gov/srd/www/x13as $\endgroup$ – Mike J Jun 9 '20 at 13:11
  • $\begingroup$ tpaker this link shows a step by step on doing a seasonal adjustment by hand (excel). Its a good walk thru catherinechhood.net/SeasAdjShortTimeSeriesExcel.pdf $\endgroup$ – Mike J Jun 10 '20 at 8:59
  • $\begingroup$ This is another good site people.duke.edu/~rnau/411seart.htm $\endgroup$ – Mike J Jun 10 '20 at 9:05
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The easy way to see the seasonal adjustment factor for many series is to divide the non-seasonally adjusted series by the seasonally adjusted version. This assumes that the seasonal adjustment factor is multiplicative.

Different series have different patterns.

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