Higher-Order estimation of s-th order spectra with flat-top lag-windows

Multivariate Lag-Windows and Group Representations

Symmetries of the auto-cumulant function (the generalization of the auto-covariance function) of a kth-order stationary time series are derived through a connection with the symmetric group of degree k. Using theory of group representations, symmetries of the auto-cumulant function are demystified and lag-window functions are symmetrized to satisfy these symmetries. A generalized Gabr-Rao optimal kernel, used to estimate general kth-order spectra, is also derived through the developed theory.

滞后窗估计量的高斯近似与谱密度置信带的构建

Gaussian Approximation for Lag-Window Estimators and the Construction of Confidence bands for the Spectral Density

本文针对平稳时间序列谱密度的同时置信带构建问题，提出用经典滞后窗谱密度估计量的高斯近似验证乘子bootstrap的渐近有效性并推导收敛速率，模拟研究验证了其有限样本性质。

Lugsail lag windows for estimating time-average covariance matrices

Lag windows are commonly used in time series, econometrics, steady-state simulation, and Markov chain Monte Carlo to estimate time-average covariance matrices. In the presence of positive correlation of the underlying process, estimators of this matrix almost always exhibit significant negative bias, leading to undesirable finite-sample properties. We propose a new family of lag windows specifically designed to improve finite-sample performance by offsetting this negative bias. Any existing lag window can be adapted into a lugsail equivalent with no additional assumptions. We use these lag win…

A general white noise test based on kernel lag-window estimates of the spectral density operator

We propose a general white noise test for functional time series based on estimating a distance between the spectral density operator of a weakly stationary time series and the constant spectral density operator of an uncorrelated time series. The estimator that we propose is based on a kernel lag-window type estimator of the spectral density operator. When the observed time series is a strong white noise in a real separable Hilbert space, we show that the asymptotic distribution of the test statistic is standard normal, and we further show that the test statistic diverges for general serially…

二次谱估计器的偏差校正

Bias correction of quadratic spectral estimators

本文将Astfalck等人针对Welch估计器的有限样本偏差校正方法扩展到滞后窗、多锥及其组合等更广泛的二次谱估计器族，并通过仿真验证了理论的有效性。