Adaptive Smoothing of the Log-Spectrum with Multiple Tapering

TL;DR

This paper introduces a hybrid method combining multiple tapering and adaptive kernel smoothing to improve the estimation of the log-spectral density of stationary time series, reducing mean square error.

Contribution

It proposes a novel hybrid estimator that enhances log-spectral density estimation by integrating multiple tapering with adaptive kernel smoothing, outperforming traditional methods.

Findings

Reduces mean square error compared to standard smoothing.

Provides a data-adaptive implementation for improved accuracy.

Demonstrates effectiveness through theoretical analysis.

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-multiple taper estimate. This procedure reduces the expected mean square error by $(\pi^2/ 4)^{4/5} $ over simply smoothing the log tapered periodogram. A data adaptive implementation of a variable bandwidth kernel smoother is given.