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基于二阶特征的局部平稳时间序列结构分类AI 解读

Abstract Time series classification is crucial for numerous scientific and engineering applications. In this article, we present a numerically efficient, practically competitive, and theoretically rigorous classification method for distinguishing between two classes of locally stationary time series based on their time-domain, second-order characteristics. Our approach builds on the autoregressive approximation for locally stationary time series, imposes no requirement on…

局部平稳时间序列的偏自相关函数：刻画、估计与推断AI 解读

SUMMARY For stationary time series, it is common to use plots of the partial autocorrelation function (PACF) or PACF-based tests to explore the temporal dependence structure of the process. To the best of our knowledge, analogues for nonstationary time series have not yet been fully developed. This article aims to fill this gap for locally stationary time series with short-range dependence. First, we characterize the PACF locally in the time domain and show that the jth PACF…

非平稳时间序列的自回归近似、推断与应用AI 解读

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time-series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent nonstationary and nonlinear time series can be well approximated globally by a white-noise-driven autoregressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a structural approximation…

非平稳时间序列精度矩阵的估计与推断AI 解读

We consider the estimation of and inference on precision matrices of a rich class of univariate locally stationary linear and nonlinear time series, assuming that only one realization of the time series is observed. Using a Cholesky decomposition technique, we show that the precision matrices can be directly estimated via a series of least squares linear regressions with smoothly time-varying coefficients. The method of sieves is utilized for the estimation and is shown to…