A0798
Title: Statistical inference of spectral density for high dimensional time series
Authors: Chi Zhang - University of California, San Diego (United States) [presenting]
Danna Zhang - University of California, San Diego (United States)
Abstract: Spectral density plays a fundamental role in time series analysis. There has been a well-developed asymptotic theory for the spectral estimates in the low-dimensional case. For high-dimensional time series, distributional theory on spectral density is still lacking. This paper aims to establish an inference theory on high dimensional spectral density. In particular, a Gaussian approximation result is established for the maximum deviation of the spectral density estimate over frequencies, which can be used to tackle a variety of time series inference problems. Furthermore, two different resampling methods are introduced to implement high-dimensional spectral inference in practice and provide theoretical justification for their validity.
