Applications of Multitaper Spectral Analysis to Nonstationary Data

Abstract

This thesis is concerned with changes in the spectrum over time observed in Holocene climate data as recorded in the Burgundy grape harvest date series. These changes represent nonstationarities, and while spectral estimation techniques are relatively robust in the presence of nonstationarity--that is, they are able to detect significant contributions to power at a given frequency in cases where the contribution to power at that given frequency is not constant over time--estimation and prediction can be improved by considering nonstationarity. We propose improving spectral estimation by considering such changes. Specifically, we propose estimating the level of change in frequency over time, detecting change-point(s) and sectioning the time series into stationary segments. We focus on locating a change in frequency domain in time, and propose a graphical technique to detect spectral changes over time. We test the estimation technique in simulation, and then apply it to the Burgundy grape harvest date series. The Burgundy grape harvest date series was selected to demonstrate the introduced estimator and methodology because the time series is equally spaced, has few missing values, and a multitaper spectral analysis, which the methodology proposed in this thesis is based on, of the grape harvest date series was recently published. In addition, we propose a method using a test for goodness-of-fit of autoregressive estimators to aid in assessment of change in spectral properties over time.

This thesis has four components: (1) introduction and study of a level-of-change estimator for use in the frequency domain change-point detection, (2) spectral analysis of the Burgundy grape harvest date series, (3) goodness-of-fit estimates for autoregressive processes, and (4) introduction of a statistical software package for multitaper spectral analysis. We present four results. (1) We introduce and demonstrate the feasibility of a level-of-change estimator. (2) We present a spectral analysis and coherence study of the Burgundy grape harvest date series that includes locating a change-point. (3) We present a study showing an advantage using multitaper spectral estimates when calculating autocorrelation coefficients. And (4) we introduce an R software package, available on the CRAN, to perform multitaper spectral estimation.