Data-Adaptive Estimation of Time-Varying Spectral Densities. Issue 2 (3rd April 2019)

• Record Type: Journal Article
• Authors: van Delft, Anne; Eichler, Michael
• Is Part Of: Journal of computational and graphical statistics. Volume 28:Issue 2(2019)
• Page Start: 244
• Page End: 255
• Publication Date: 2019-04-03
• Subjects: Data-adaptive kernel estimation -- Local stationary processes; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2018.1512866
• Languages: English
• ISSNs: 1061-8600

Abstract

ABSTRACT: This article introduces a data-adaptive nonparametric 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, 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. Supplementary materials, including the R package tvspecAdapt containing an implementation of the routine, are available online.