IEEE Trans Neural Netw Learn Syst. 2012 Oct;23(10):1564-73. doi: 10.1109/TNNLS.2012.2207739.
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.
对于期货合约价格的时间序列，预期价格变化是根据过去的价格变化来建模的。所提出的模型采用在再生核希尔伯特空间中的回归形式，其约束条件是回归函数必须是奇数。通过对核的适当修改，可以将由此产生的约束优化问题简化为无约束问题。特别是，通过分别的对称约束来展示如何自然地出现奇数、偶数和其他类似的核，作为相应的希尔伯特子空间的再生核。为了测试奇数假设的有效性和实际有用性，在四个期货合约的大型真实数据集上进行了实验，结果表明使用奇数核可以提高预测精度，并减少过度拟合的趋势。
