Adaptive Kernel Estimation of the Spectral Density with Boundary Kernel Analysis

TL;DR

This paper introduces a hybrid method combining multitaper estimation and adaptive kernel smoothing to improve spectral density estimation accuracy for stationary time series, especially near discontinuities.

Contribution

It proposes a novel hybrid estimator that reduces mean square error and includes a data adaptive variable bandwidth kernel smoothing approach for boundary handling.

Findings

Reduces mean square error by approximately 20% compared to traditional methods.

Provides an optimal number of tapers proportional to N^{8/15}.

Includes a practical adaptive implementation for discontinuous spectral densities.

Abstract

A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate. This procedure reduces the expected mean square error by $({\pi^2 \over 4})^{.8}$ over simply smoothing the log tapered periodogram. The optimal number of tapers is $O(N^{8/15})$. A data adaptive implementation of a variable bandwidth kernel smoother is given. When the spectral density is discontinuous, one sided smoothing estimates are used.