标题： 一个针对协变量依赖时间序列的高效谱分析的倒谱模型 显示英文标题

标题： A Cepstral Model for Efficient Spectral Analysis of Covariate-dependent Time Series

摘要： 本文介绍了一种新颖且计算快速的模型，用于研究协变量与复制时间序列功率谱之间的关联。 使用随机协变量依赖的Cramér谱表示和半参数对数谱模型来量化对数谱与协变量之间的关联。 每个复制特定的对数谱由倒谱表示，从而生成以倒谱系数为响应的基于倒谱的多元线性模型。 通过仅使用少量倒谱系数，该模型简洁地捕获了时间序列的频率模式，并且相比现有方法节省了大量的计算时间。 提出了一种两阶段估计程序。 在第一阶段，采用基于Whittle似然的方法估计截断的复制特定的倒谱系数。 在第二阶段，估计基于倒谱的多元线性模型的参数，进而估计协变量的影响函数。 该模型具有灵活性，可以根据应用、领域知识或协变量特征选择多种多元线性模型的估计方法。 数值研究表明，尽管该方法简单且计算时间较短，但它比一些现有方法表现更好。 本文的补充材料可在线获取。 显示英文摘要

摘要： This article introduces a novel and computationally fast model to study the association between covariates and power spectra of replicated time series. A random covariate-dependent Cram\'{e}r spectral representation and a semiparametric log-spectral model are used to quantify the association between the log-spectra and covariates. Each replicate-specific log-spectrum is represented by the cepstrum, inducing a cepstral-based multivariate linear model with the cepstral coefficients as the responses. By using only a small number of cepstral coefficients, the model parsimoniously captures frequency patterns of time series and saves a significant amount of computational time compared to existing methods. A two-stage estimation procedure is proposed. In the first stage, a Whittle likelihood-based approach is used to estimate the truncated replicate-specific cepstral coefficients. In the second stage, parameters of the cepstral-based multivariate linear model, and consequently the effect functions of covariates, are estimated. The model is flexible in the sense that it can accommodate various estimation methods for the multivariate linear model, depending on the application, domain knowledge, or characteristics of the covariates. Numerical studies confirm that the proposed method outperforms some existing methods despite its simplicity and shorter computational time. Supplementary materials for this article are available online.