Bandwidth selection for kernel estimate with correlated noise

The problem of selecting the bandwidth for the kernel estimate is considered. It is shown that Mallows' criterion does not select a proper bandwidth when the noise are correlated. A simple modification of Mallows' criterion is suggested, which significantly improves the performance of the kernel estimate. Since the modified criterion needs an estimate for the noise spectrum at frequency zero, an estimation procedure for the parameter of the noise spectrum is proposed. Under some regularity conditions, it is shown that the procedure gives strongly consistent estimates. The asymptotic distribution of the estimate is also given.