Tree-Structured Wavelet Thresholding for Estimation of Evolutionary Spectra

• Activity Number: 327
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Rainer Von Sachs*+
• Keywords: Tree structure ; wavelets ; time-varying spectrum ; locally stationary process ; factor analysis ; 2D-smoothing

Abstract

In this talk we present a new approach to adaptively estimate an evolutionary spectrum of a locally stationary process by a generalization of the recently developed tree-structured wavelet estimator of Freyermuth et al (JASA 2010, EJS 2011) to a 2-dimensional smoother over time and frequency. This approach appears as a more practical compromise between a fully non-linear threshold estimator advertised in Neumann and von Sachs (AoS 1998) and a non-adaptive linear (kernel) smoother. We will outline the background of tree-structured wavelet thresholding and also mention possible applications to time-varying factor analysis of economical or financial time series panels, as developed recently by Eichler, Motta and von Sachs (J. Econometrics 2011). Time permitting, we discuss its potential for the development of a segmented factor analysis, with loadings that behave approximately stationary over segments of time-constancy between breakpoints - potentially caused by external market events such as political, financial or environmental crises, changing monetary policy decisions and alike. Part of this work is joint with Jean-Marc Freyermuth (ECON, KU Leuven, BELGIUM).