These predictions do not yet take into account short term variations caused by the sun's rotation. Original data from Navy program called MICA for the period 1990-2005
The sun is not the center of mass of the solar system. The center of mass of the solar system -- its barycenter -- is slightly offset from the center of the sun. This is caused by the gravitational pull of the planets -- primarily Jupiter.
As the sun spins on its axis, the core interacts with the outer plasma envelope. It is kind of like scraping the core as a wood plane scrapes off wood chips -- only this happens electromagnetically. Because the sun is orbiting the Barycenter, the force of interaction between the core and envelope varies over the sunspot cycle. As the force increases, waves on the core become more powerful, inducing balls-of-light (sunspots) that decay.
You can easily see the most basic correlation here.
There is not much to say here.
The correlation here is exact with the last midpoint of the peak of cycle 22 and the last minimum between cycles 22 and 23 -- the current sunspot cycle. This leads to the prediction that the center of cycle 23 will occur about 8/29/2004.
Plotting changes in acceleration is very revealing.
This particular chart has an inverse relationship -- as the chart dips below the black line sunspots will, in general, get worse. The overall dip of the black line to the right represents energy being released from the sun over the entire sunspot cycle. The bigger the drop, the more energy released by the core of the sun. Rising points represent where the planets are pulling the sun away from barycenter, in essence inputting potential energy into the sun.
The following animation has its peaks reversed from above.
Again, these predictions do not take into account the short term variations caused by the sun's rotation.
There is a web-site called Solar System Live. It shows the positions of the planets. By analyzing the positions of the planets, it is possible to simply look at the planets positions and predict sunspots.
An animation that I made, using Solar System Live images, on the same key dates as the above animation, allows you to visually see this process.