高维谱密度矩阵的柔性非线性推理与变点测试

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Ansgar Steland
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引用次数: 0

摘要

本文研究了一种基于双线性形式的谱平均统计量计算的线性统计量和滞后窗(即带正则化)谱密度矩阵估计量的非线性变换来分析无约束维高维非线性时间序列的灵活方法。这类统计包括平滑周期图、非线性统计(如相干性)、长期运行方差估计和与因子效应相关的对比统计(作为特殊情况)。特别地,我们引入了谱密度矩阵的一类非线性谱平均。考虑到大数据环境,我们研究了一种包括稀疏采样方案的采样设计。针对这些频域统计量和非平稳下的滞后窗(交叉)谱估计量,导出了具有最优速率的非线性时间序列高斯逼近。对于变更测试(自我标准化),将检查CUSUM统计数据。进一步,提出了一种特定的野自举方法来估计临界值。本文的补充部分提供了对标准普尔500指数财务回报的模拟研究和应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Flexible nonlinear inference and change-point testing of high-dimensional spectral density matrices

This paper studies a flexible approach to analyze high-dimensional nonlinear time series of unconstrained dimension based on linear statistics calculated from spectral average statistics of bilinear forms and nonlinear transformations of lag-window (i.e. band-regularized) spectral density matrix estimators. That class of statistics includes, among others, smoothed periodograms, nonlinear statistics such as coherency, long-run-variance estimators and contrast statistics related to factorial effects as special cases. Especially, we introduce the class of nonlinear spectral averages of the spectral density matrix. Having in mind big data settings, we study a sampling design which includes a sparse sampling scheme. Gaussian approximations with optimal rate are derived for nonlinear time series of growing dimension for these frequency domain statistics and the underlying lag-window (cross-) spectral estimator under non-stationarity. For change-testing (self-standardized) CUSUM statistics are examined. Further, a specific wild bootstrap procedure is proposed to estimate critical values. Simulation studies and an application to SP500 financial returns are provided in a supplement to this paper.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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