Modified nonparametric spectral density estimation under long-range dependence

초록

The spectral density of the time series analysis under long-range dependence (LRD) is an important area in investigating the properties of the parameter estimators of interest and observing the periodic characteristics of the time series data. As model assumptions of time-dependent data strongly influence the time series analysis, the paper proposed modification techniques of nonparametric spectral density estimation under long-range dependence to consider the boundary effects using periodicity characteristics of the periodograms and spectral density in the frequency domain. We demonstrated the uniform and pointwise consistency of the modified version of nonparametric spectral density estimator (NPSDE) under LRD satisfying mild conditions. We also provided the uniform and pointwise optimal bandwidth orders to minimize the uniform and pointwise absolute relative estimation errors, respectively. Numerical studies were carried out to compare the general NPSDE under LRD and the modified version of NPSDE under LRD.

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