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高维时间序列因子模型的权重校准估计AI 解读

The factor modeling for high-dimensional time series is powerful in discovering latent common components for dimension reduction and information extraction. Most available estimation methods can be divided into two categories: the covariance-based under asymptotically-identifiable assumption and the autocovariance-based with white idiosyncratic noise. This paper follows the autocovariance-based framework and develops a novel weight-calibrated method to improve the estimation…

高维函数时间序列的因子建模AI 解读

Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables p diverges as the number of serially dependent observations n increases. In this paper, we present a novel functional factor model for high-dimensional functional time series that maintains and makes use of the functional and dynamic structure to achieve great dimension reduction and find the latent factor structure. To estimate the…

高维函数型时间序列的建模与预测AI 解读

We propose a two-step procedure to model and predict high-dimensional functional time series, where the number of function-valued time series p is large in relation to the length of time series n. Our first step performs an eigenanalysis of a positive definite matrix, which leads to a one-to-one linear transformation for the original high-dimensional functional time series, and the transformed curve series can be segmented into several groups such that any two subseries from…

条件函数稀疏性下大型协方差矩阵函数的因子引导估计AI 解读

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar loadings or scalar factors with functional loadings, and postulate functional sparsity on the covariance of idiosyncratic errors after taking out the common unobserved factors. To facilitate estimation, we rely on the spiked matrix model…

高维稀疏协方差函数估计的自适应函数阈值法AI 解读

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications.In this article, we consider estimating sparse covariance functions for high-dimensional functional data, where the number of random functions p is comparable to, or even larger than the sample size n.Aided by the Hilbert-Schmidt norm of functions, we introduce a new class of functional thresholding operators that combine functional versions of…

基于自协方差的高维函数型时间序列学习框架AI 解读

Many scientific and economic applications involve the statistical learning of high-dimensional functional time series, where the number of functional variables is comparable to, or even greater than, the number of serially dependent functional observations. In this paper, we model observed functional time series, which are subject to errors in the sense that each functional datum arises as the sum of two uncorrelated components, one dynamic and one white noise. Motivated…

函数型线性回归：序列依赖与误差污染AI 解读

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by iid measurement errors. In practice, however, the dynamical dependence across different curves may exist and the parametric assumption on the error covariance structure could be unrealistic. In this article, we…

面板数据单指标模型中的同质结构识别AI 解读

Panel data analysis is an important topic in statistics and econometrics. Traditionally, in panel data analysis, all individuals are assumed to share the same unknown parameters, e.g. the same coefficients of covariates when the linear models are used, and the differences between the individuals are accounted for by cluster effects. This kind of modelling only makes sense if our main interest is on the global trend, this is because it would not be able to tell us anything…

高维双重函数型图模型AI 解读

Summary We consider estimating a functional graphical model from multivariate functional observations. In functional data analysis, the classical assumption is that each function has been measured over a densely sampled grid. However, in practice the functions have often been observed, with measurement error, at a relatively small number of points. We propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a…

函数型图模型AI 解读

Graphical models have attracted increasing attention in recent years, especially in settings involving high-dimensional data. In particular, Gaussian graphical models are used to model the conditional dependence structure among multiple Gaussian random variables. As a result of its computational efficiency, the graphical lasso (glasso) has become one of the most popular approaches for fitting high-dimensional graphical models. In this paper, we extend the graphical models…