What you're doing is not autocorrelation (which would produce values between -1 and 1), but I still wondered why you were coming up with the discrepancy. It turns out that you are not that far off from Jose--even though the abstract reports the period as 178.7 years, his calculation of the period of R, which corresponds to your calculation, is 178.81 years (see Table II), with a standard deviation of .32, so your value of 178.86 is not in disagreement.

Jose just combines all of the periods into a single estimate of 178.77--and noticing that that's essentially the period of 9xJS (which he calculates as 178.72), he rounds it off to 178.7. But his calculation is virtually identical to yours.From the table, the 9xJS value only provides 41% of the power of the signal. I did more work on this table to show the integer multiples of each subwave that are closest to 179, as follows.

(Note due to the coding format the letters in the list at the top match to the text in the following line, eg % of total spectrum is explained by E in the notes at the bottom).Code:Fourier Spectrum Decomposition of Wave Function of Solar System Barycentre Cycle SSB Spectral Peak (Years) A First Planet B Second Planet C Spectral Power D % of total spectrum E Orbital Period F Cycle period close to 179 years G Cycles in 178.86 years H Rounded # of cycles I Absolute Variance from 178.86 J Precession Ratio K 1 19.85 Jupiter Saturn 983 40.9% 19.85 178.67 9.010 9 0.11% 144.24 2 12.8 Jupiter Neptune 419 17.4% 12.78 178.92 13.996 14 0.03% 144.04 3 13.8 Jupiter Uranus 190 7.9% 13.81 179.52 12.952 13 0.37% 143.55 4 35.9 Saturn Neptune 189 7.9% 35.87 179.36 4.986 5 0.28% 143.68 5 11.9 Jupiter Cycle 137 5.7% 11.86 177.90 15.081 15 0.54% 144.86 6 7.8 unknown 128 5.3% 7.80 179.40 22.931 23 0.30% 143.65 7 45.5 Saturn Uranus 96 4.0% 45.37 181.48 3.942 4 1.44% 142.01 8 9.9 Jupiter Saturn 75 3.1% 9.93 178.67 18.019 18 0.11% 144.24 9 8.2 unknown 72 3.0% 8.20 180.40 21.812 22 0.85% 142.86 10 29.5 Saturn cycle 59 2.5% 29.46 176.76 6.071 6 1.19% 145.80 11 171 Uranus Neptune 57 2.4% 171.37 171.37 1.044 1 4.37% 150.39 Source Fourier Transform E= D/SUM(D) F = 1/(1/B - 1/C) G= F x I H= 178.86/F I= round(H) J= ABS(H/I-1) K= 25771/G

As I mentioned earlier, there are three subwaves , JN, JU and SN, which have integer multiples just above 179. With JS contributing 41%, and these three contributing 33%, it makes sense that the overall wave period would sit in between these main groups, as I found by the autocorrelation of the wave form.

So why is it even that much greater than 178.73, the value we calculated for 9xJS. I suspect it is the influence of Neptune, and Uranus. The UN synodic period is 171.393, which is just shy of 178.73. Integrated over a complete cycle, the cross correlation should be zero, but you're integrating over 6000 years, just like Jose (which is why you get the same answer 178.86 as he does 178.81, both larger than 178.73). A complete JS/UN cycle would be complete in 178.73381/(178.73381-171.393)*178.73381 or 4351.8 years. Try re-doing your calculation with just the last 4352 years of data (or the first 4352, or any set of 4352 years inbetween), and see what value that you get.