SSN with various filters

Figure 1. An example of spurious results produced by simple running mean “smoothers”, compared to other, better filters and the unsmoothed monthly averages.

The filters used are simple running mean of 12 months, triple running mean of 5 months and a 3-sigma gaussian with sigma=2mo.

It can be noted that the 5 month filter does a better job of “smoothing” the data than the 12 month running mean.

The official NOAA/Space Weather Prediction Center presentation shows “smoothed monthly values” here:
http://www.swpc.noaa.gov/SolarCycle/index.html

In the comparison shown in figure 1 it would appear they are using the classic 12mo running mean to distort their data. The data presented by NOAA seems to be the same “smoothed” monthly values provided by Royal Observatory of Belgium http://sidc.oma.be/ that host the global reference for sunspot data: SIDC ftp://omaftp.oma.be/dist/astro/sidcdata/

SIDC readme file indicates a 13 point filter with first and last points weighted 50%. This is only a slight improvement on a flat running mean.
http://sidc.oma.be/html/readme.txt

In a way that is very common with simple running mean, the real peak gets inverted and is not the peak in the “smoothed” data. A false peak is created about four months later during a dip in the original data, which was actually the lowest monthy value in the last 2.5 years, not the peak.

This graph accompanies an article on filter distortion:
https://climategrog.wordpress.com/2013/05/19/triple-running-mean-filters/

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