Data-adaptive estimation of time-varying spectral densities

TL;DR

This paper presents a data-adaptive non-parametric method for estimating time-varying spectral densities that automatically adjusts smoothing kernels based on local data features, improving flexibility and accuracy.

Contribution

It introduces an iterative, data-driven algorithm for constructing localized smoothing kernels, eliminating the need for manual bandwidth selection in spectral density estimation.

Findings

The method adapts to changing spectral curvature.

It effectively detects and adjusts for structural breaks.

Performance surpasses traditional fixed-bandwidth approaches.

Abstract

This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The performance of these nonparametric estimators, however, depends crucially on the smoothing bandwidths that need to be specified in both time and frequency direction. As an alternative and extension to traditional bandwidth selection methods, we propose an iterative algorithm for constructing localized smoothing kernels data-adaptively. The main idea, inspired by the concept of propagation-separation (Polzehl and Spokoiny 2006), is to determine for a point in the time-frequency plane the largest local vicinity over which smoothing is justified by the data. By shaping the smoothing kernels nonparametrically, our method not only avoids the problem of bandwidth selection in the strict sense but also becomes more flexible. It not only adapts to changing curvature in smoothly varying spectra but also adjusts for structural breaks in the time-varying spectrum.