Kernel Regression with Correlated Errors

It is a well-known problem that obtaining a correct bandwidth in nonparametric regression is difficult in the presence of correlated errors. There exist a wide variety of methods coping with this problem, but they all critically depend on a tuning procedure which requires accurate information about the correlation structure. Since the errors cannot be observed, the latter is a hard goal to achieve. In this paper, we show the breakdown of several data-driven parameter selection procedures. We also develop a bandwidth selection procedure based on bimodal kernels which successfully removes the error correlation without requiring any prior knowledge about its structure. Some extensions are made to use such a criterion in least squares support vector machines for regression.