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高维时间序列预测回归中有效协整秩的确定AI 解读

This article proposes a new approach to identifying the effective cointegration rank in high-dimensional unit-root (HDUR) time series from a prediction perspective using reduced-rank regression. For a HDUR process xt∈RN and a stationary series yt∈Rp of interest, our goal is to predict future values of yt using xt and lagged values of yt. The proposed framework consists of a two-step estimation procedure. First, the Principal Component Analysis is used to identify all…

监督式动态主成分分析：多预测变量下的线性动态预测AI 解读

This paper proposes a novel dynamic forecasting method using a new supervised Principal Component Analysis (PCA) when a large number of predictors are available. The new supervised PCA provides an effective way to bridge the gap between predictors and the target variable of interest by scaling and combining the predictors and their lagged values, resulting in an effective dynamic forecasting. Unlike the traditional diffusion-index approach, which does not learn the…

分而治之：大规模时间序列的分布式层级因子建模AI 解读

This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using Principal Component Analysis (PCA) and shows great promises for modeling large-scale data that cannot be stored nor analyzed by a single machine. Each computer at the basic level performs a PCA to extract common factors among the time…

高维向量自回归模型的速率最优稳健估计AI 解读

High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series, but also the existence of aberrant observations, such as missing values, contaminated observations, and heavy-tailed distributions. For high-dimensional vector autoregressive (VAR) models, we introduce a unified estimation procedure that is…

促进大规模状态空间模型简约性的先验AI 解读

State–space models are commonly used in the engineering, economic, and statistical literature. They are flexible and encompass many well-known statistical models, including random coefficient autoregressive models and dynamic factor models. Bayesian analysis of state–space models has attracted much interest in recent years. However, for large scale models, prior specification becomes a challenging issue in Bayesian inference. In this paper, we propose a flexible prior for…

高维时间序列建模：动态相依因子与发散特征值AI 解读

This article proposes a new approach to modeling high-dimensional time series by treating a p-dimensional time series as a nonsingular linear transformation of certain common factors and idiosyncratic components. Unlike the approximate factor models, we assume that the factors capture all the nontrivial dynamics of the data, but the cross-sectional dependence may be explained by both the factors and the idiosyncratic components. Under the proposed model, (a) the factor…

高维时间序列数据的序列相关与 ARCH 效应检验AI 解读

This article proposes several tests for detecting serial correlation and ARCH effect in high-dimensional data. The dimension of data p=p(n) may go to infinity when the sample size n→∞

基于极值理论的高维时间序列序列相关检验AI 解读

This paper proposes a simple test for detecting serial correlations in high-dimensional time series. The proposed test makes use of the robust properties of Spearman’s rank correlation and the theory of extreme values. Asymptotic properties of the test statistics are derived under some minor conditions as both the sample size and dimension go to infinity. The test is not sensitive to the underlying distribution of the time series so long as the data are continuously…

高维矩阵值时间序列的约束因子模型AI 解读

High-dimensional matrix-variate time series data are becoming widely available in many scientific fields, such as economics, biology, and meteorology. To achieve significant dimension reduction while preserving the intrinsic matrix structure and temporal dynamics in such data, Wang, Liu, and Chen proposed a matrix factor model, that is, shown to be able to provide effective analysis. In this article, we establish a general framework for incorporating domain and prior…

基于距离协方差的独立成分分析AI 解读

This article introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating mutually independent components, and a versatile resampling-based procedure for inference, including misspecification testing. Independent components are estimated by combining a nonparametric probability integral transformation with a generalized nonparametric whitening method based on distance covariance that…

结构化相关矩阵建模AI 解读

Ensuring positive definiteness of an estimated structured correlation matrix is challenging. We show that reparameterizing Cholesky factors of correlation matrices using hyperspherical coordinates or angles provides a flexible and effective solution. Once a structured correlation matrix is identified, the corresponding angles and hence the constrained correlations may be estimated by maximum likelihood. Consistency and asymptotic normality of the maximum likelihood…

分析大规模依赖数据的若干方法AI 解读

We consider an approach to analyze big data of time series. Big dependent data are first transformed into functional time series of densities via nonparametric density estimation. We then discuss some tools for exploratory data analysis of the resulting functional time series. The tools employed include K-means cluster analysis and tree-based classification. For modeling, we propose a threshold approximate-factor model and a Hellinger distance autoregressive model for…

高维动态随机 Copula 模型AI 解读

We build a class of copula models that captures time-varying dependence across large panels of financial assets. Our models nest Gaussian, Student’s t, grouped Student’s t, and generalized hyperbolic copulas with time-varying correlations matrices, as special cases. We introduce time-variation into the densities by writing them as factor models with stochastic loadings. The proposed copula models have flexible dynamics and heavy tails yet remain tractable in high dimensions…

回应AI 解读

We express our sincere thanks to all the discussants for their constructive discussions and encouragement. In particular, we appreciate their proposals of alternative approaches to finding common v...

主波动率成分分析AI 解读

Many empirical time series such as asset returns and traffic data exhibit the characteristic of time-varying conditional covariances, known as volatility or conditional heteroscedasticity. Modeling multivariate volatility, however, encounters several difficulties, including the curse of dimensionality. Dimension reduction can be useful and is often necessary. The goal of this article is to extend the idea of principal component analysis to principal volatility component…

多变量时间序列的动态正交成分AI 解读

We introduce dynamic orthogonal components (DOC) for multivariate time series and propose a procedure for estimating and testing the existence of DOCs for a given time series. We estimate the dynamic orthogonal components via a generalized decorrelation method that minimizes the linear and quadratic dependence across components and across time. We then use Ljung–Box type statistics to test the existence of dynamic orthogonal components. When DOCs exist, univariate analysis…

受约束因子模型AI 解读

This article considers estimation and applications of constrained and partially constrained factor models when the dimension of explanatory variables is high. Both the classical and approximate factor models are investigated. For estimation, we employ both the maximum likelihood and least squares methods. We show that the least squares estimation is based on constrained principal component analysis and provides consistent estimates for the model under certain conditions. The…

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日频股票波动率的长程依赖AI 解读

Recent empirical studies show that the squares of high-frequency stock returns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Are such long-range dependencies common among stocks? Are they caused by the same sources of variation? In this article, we classify daily stock returns of Standard and Poor 500 companies on the basis of a company's size and its business or industrial…

多元门限模型的检验与建模AI 解读

Threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years. In this article I use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model. The thresholds and the model are selected jointly based on the Akaike information criterion. The finite-sample performance of the…

识别多元时间序列模型的统一方法AI 解读

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…

美国失业率预测AI 解读

This article presents a comparison of forecasting performance for a variety of linear and nonlinear time series models using the U.S. unemployment rate. Our main emphases are on measuring forecasting performance during economic expansions and contractions by exploiting the asymmetric cyclical behavior of unemployment numbers, on building vector models that incorporate initial jobless claims as a leading indicator, and on utilizing additional information provided by the…

多元时间序列模型识别的统一方法AI 解读

This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing.…