Bayesian Nonparametric Spectral Analysis of Locally Stationary Processes
针对局部平稳过程，提出一种动态Whittle似然近似和贝叶斯非参数方法，用于估计时变谱密度，并证明了后验一致性和收缩率，模拟和实际数据表现优于现有方法。
Stationarity plays a pivotal role in time series analysis. It is not only the basis for the derivation of general asymptotic theory but it also allows an efficient analysis in the frequency domain via the Whittle likelihood, based on the asymptotic independence of the Fourier coefficients. However, many regularly sampled data derived from the observation of physical or ecological processes, for instance, are only locally stationary. They exhibit slowly evolving spectra and asymptotically non-vanishing dependencies between the Fourier coefficients. In this paper we construct a novel dynamic Whittle likelihood approximation for a locally stationary process and propose a Bayesian nonparametric approach to estimate its time-varying spectral density. This dynamic likelihood approximation in the frequency domain can capture the time-frequency evolution of the process by using moving periodograms previously introduced in the bootstrap literature. The posterior distribution is obtained by updating a bivariate extension of the Bernstein-Dirichlet process prior with the dynamic Whittle likelihood. Asymptotic properties such as sup-norm posterior consistency and L2-norm posterior contraction rates are presented. In addition, simulation studies and applications to real-life datasets demonstrate the competitive empirical performance compared to other state-of-the-art methods under finite-sample conditions.