Reproducing kernel Hilbert spaces with odd kernels in price prediction.

For time series of futures contract prices, the expected price change is modeled conditional on past price changes. The proposed model takes the form of regression in a reproducing kernel Hilbert space with the constraint that the regression function must be odd. It is shown how the resulting constrained optimization problem can be reduced to an unconstrained one through appropriate modification of the kernel. In particular, it is shown how odd, even, and other similar kernels emerge naturally as the reproducing kernels of Hilbert subspaces induced by respective symmetry constraints. To test the validity and practical usefulness of the oddness assumption, experiments are run with large real-world datasets on four futures contracts, and it is demonstrated that using odd kernels results in a higher predictive accuracy and a reduced tendency to overfit.