A fundamental problem in time series analysis is estimation of the spectral density. Parametric estimators, such as those from autoregressive moving average models, use only a finite number of parameters. When parametric models are not appropriate a nonparametric approach can be utilized that is based on nonparametric smoothers that are applied to the sample periodogram.;In this dissertation, a new kernel based estimator of the spectral density is proposed along with two associated methods for global and local bandwidth selection. The large sample properties of the kernel estimator and bandwidth selectors are derived and the performance of the kernel approach relative to local polynomial estimators is investigated via empirical comparisons. The results suggest that the kernel and local polynomial estimation methods give similar results in terms of average (across the design) mean squared error. However, the kernel approach has the advantage of being readily available through a simple modification of existing R software.;The last topic that is considered is testing the hypothesis that a time series is white noise. A new test is developed for this purpose and its large sample properties are established under both the null and alternative hypotheses. Empirical comparisons with the widely used Bartlett and Q tests indicate that the new test outperforms the Q test and is competitive with Bartlett's procedure.
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