<p>Examples of actual seasonal adjustment curves continue to be ridiculously difficult to find. The only example that I was able to find were from <a href="https://people.duke.edu/%7Ernau/411seas.htm" rel="nofollow noreferrer">these lecture notes</a> by Prof. Robert Nau of Duke University's Fuqua School of Business, which applies to the time series of total U.S. retail automobile sales (dollar value, not number of units sold) between January 1970 and May 1998:
<a href="https://i.sstatic.net/A2NAyEy8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/A2NAyEy8.png" alt="enter image description here" /></a></p>
<p>I am at a complete loss for an explanation why, out of the zillions of online explanations that found of how to calculate the seasonal adjustment indices (using multiplicative adjustment) for a time series, none of them (except for this one) actually show what the resulting curve looks like.</p>

CC BY-SA 4.0
2024-08-10T02:14:33.930Z
2024-08-10T02:14:33.930Z
tparker
<p>Quarterly GDP seasonally adjusted
<a href="https://i.sstatic.net/Jev92.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Jev92.png" alt="enter image description here"></a></p>

<p>source:  <a href="https://aneconomicsense.org/category/econ-data/gdp-productivity/" rel="nofollow noreferrer">https://aneconomicsense.org/category/econ-data/gdp-productivity/</a>
AnEconomicSense.org by Frank Lysy </p>

<p>Monthly unemployment rate seasonally adjusted</p>

<p><a href="https://i.sstatic.net/JqmiJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/JqmiJ.png" alt="enter image description here"></a></p>

<p>Source: <a href="https://www.researchgate.net/figure/Seasonal-adjustment-of-US-unemployment-using-the-defaults-of-seasonal-The-result-is_fig2_329822239" rel="nofollow noreferrer">https://www.researchgate.net/figure/Seasonal-adjustment-of-US-unemployment-using-the-defaults-of-seasonal-The-result-is_fig2_329822239</a>
by  Christoph Sax and Dirk Eddelbuettel</p>

<p>These are just some examples.  </p>

<p><strong>To manually do it in excel this link  from Catherine Hood shows an example</strong>   </p>

<p><a href="http://www.catherinechhood.net/SeasAdjShortTimeSeriesExcel.pdf" rel="nofollow noreferrer">http://www.catherinechhood.net/SeasAdjShortTimeSeriesExcel.pdf</a></p>

<p>simplest case- – <strong><em>A Quarterly Series with a Flat Trend</em></strong></p>

<p>Steps to calculate the seasonal adjustment:</p>

<ol>
<li><p>Calculate the average for the series. This will be use as the trend.</p></li>
<li><p>Calculate the difference between the original series and the trend. Label this as "residual"</p></li>
<li><p>Calculate the seasonal factors (SF), which are the average of the residuals for a given quarter.</p></li>
</ol>

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

<ol start="4">
<li>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.</li>
</ol>

CC BY-SA 4.0
2020-06-09T12:31:13.550Z
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.
tparker
CC BY-SA 4.0
2020-06-09T13:11:17.573Z
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 https://www.census.gov/srd/www/x13as/
Mike J
CC BY-SA 4.0
2020-06-10T08:59:18.120Z
tpaker this link shows a step by step on doing a seasonal adjustment by hand (excel).  Its a good walk thru  http://www.catherinechhood.net/SeasAdjShortTimeSeriesExcel.pdf
Mike J
CC BY-SA 4.0
2020-06-10T09:05:48.273Z
This is another good site https://people.duke.edu/~rnau/411seart.htm
Mike J
CC BY-SA 4.0
2020-06-09T03:04:48.493Z
2020-06-10T09:05:00.173Z
2020-06-10T09:05:00.173Z
Mike J
<p>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.</p>

<p>Different series have different patterns.</p>

CC BY-SA 4.0
2020-05-09T22:28:58.083Z
2020-05-09T22:28:58.083Z
Brian Romanchuk
<p>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.</p>

<p>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.</p>

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

CC BY-SA 4.0
2020-06-09T02:41:21.890Z
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.
Mike J
CC BY-SA 4.0
2020-06-09T03:03:19.240Z
@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.
tparker
<macroeconomics><econometrics><gdp><data-request><unemployment>
What does the seasonal adjustment curve for major macroeconomic metrics look like?
tparker
# What does the seasonal adjustment curve for major macroeconomic metrics look like?

(Asked by: username_0 on 2020-05-09)

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.)

**Tags:** macroeconomics, econometrics, gdp, data-request, unemployment
> **Comments:**
> **username_1**: 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.  
> **username_0**: @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.  

---

## 3 answers

### Answer by username_0 on 2024-08-10. Score: 0 | Accepted answer

Examples of actual seasonal adjustment curves continue to be ridiculously difficult to find. The only example that I was able to find were from [these lecture notes](https://people.duke.edu/%7Ernau/411seas.htm) by Prof. Robert Nau of Duke University's Fuqua School of Business, which applies to the time series of total U.S. retail automobile sales (dollar value, not number of units sold) between January 1970 and May 1998:
[![enter image description here](https://i.sstatic.net/A2NAyEy8.png)](https://i.sstatic.net/A2NAyEy8.png)

I am at a complete loss for an explanation why, out of the zillions of online explanations that found of how to calculate the seasonal adjustment indices (using multiplicative adjustment) for a time series, none of them (except for this one) actually show what the resulting curve looks like.


---

### Answer by username_1 on 2020-06-09. Score: 2

Quarterly GDP seasonally adjusted
[![enter image description here](https://i.sstatic.net/Jev92.png)](https://i.sstatic.net/Jev92.png)

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

Monthly unemployment rate seasonally adjusted

[![enter image description here](https://i.sstatic.net/JqmiJ.png)](https://i.sstatic.net/JqmiJ.png)

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.

4. 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.

> **Comments:**
> **username_0**: 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.  
> **username_1**: 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 https://www.census.gov/srd/www/x13as/  
> **username_1**: tpaker this link shows a step by step on doing a seasonal adjustment by hand (excel).  Its a good walk thru  http://www.catherinechhood.net/SeasAdjShortTimeSeriesExcel.pdf  
> **username_1**: This is another good site https://people.duke.edu/~rnau/411seart.htm  

---

### Answer by username_2 on 2020-05-09. Score: 0

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.


---

