Local cross validation for spectrum bandwidth choice

We investigate an automatic method of determining a local bandwidth for nonparametric kernel spectral density estimates at a single frequency. This procedure is a modification of a cross-validation tecnique for global bandwidth choices, avoiding the computation of any pilot estimate based on initial bandwidths or on approximate parametric models. Only local conditions on the spectral density around the frequency of interest are assumed. We illustrate with a Monte CarIo study the performance in finite samples of the bandwidth estimates proposed.