I've looked at kernel regression but never tried to implement it. There's many ways to define non-linearity. I lean toward a complex ruleset that encompasses more than 3 dimensions. By trial and error I match rules striving for a best fit and alter the combinations based on the results. It's my impression the trader I know that suggested non-linearity used a proprietary software platform that was able to optimize an infinite number of variable combinations... by spitting out reiterations until it achieved perfection. This might be considered a curve fitting approach but not when used to combine valid rules.
However even optimizing parameters would work successfully if the optimization engine was capable of true multi dimensional optimization. In 2D an optimization that results in a bell curve isn't curve fitting. In 3D a true multi dimensional optimization results in a perfect conic sphere, almost a perfect cone but with a flat spot at the top similar to what's needed with a good bell curve since the nearest neighbors are also good matches. The true 3D approach results in 2 bell curves at 90 degree angles to each other that's why a conic sphere is preferable over a cone. The optimization engine he used was capable of reiterating until it achieved this perfection... and it worked beyond 3D into 4,5,6 dimensions. I don't believe there were any limits. The key to it of course was it's ability to consider all the combinations simultaneously rather than going down through the list in simple sequential pairs. That doesn't work.
Not a whole lot about non-linearity there but if you consider a database with 10 dimensions and run the optimization I described then you've got the non-linearity I'm picturing.
I've heard good things about kernel regression. If you decide to pursue it I'm interested in hearing more about it. I'm even interested in coding it! ... but not sure my software is capable of it. TS2000i.
Best regards, MM
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