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流形值时间序列的黎曼因子模型AI 解读

We propose a Riemannian factor model (RFM), a novel framework for analyzing potentially high-dimensional time series data observed on Riemannian manifolds. Such time series are encountered in various applications, including economics, finance, medical imaging, and genomics and microbiome research. The proposed model is geometry-aware and accounts for the inherent nonlinearity in the data. In a high-dimensional asymptotic regime, where the manifold dimension is allowed to…

用 BAND 缓解维度灾难：高维非参数分布估计AI 解读

Minimax-optimal rates for multivariate distribution estimation are known to suffer from the curse of dimensionality. We propose a sparse Bayesian network approach in which each conditional probability is estimated using sparsity-aware conditional mean methods. The resulting estimator, \textit{BAyesian Network Distribution regression} (BAND), handles mixed data types in high-dimensional time series and achieves polynomial total variation convergence rates while allowing the…

具有大量预测变量的单位根时间序列模型选择AI 解读

This paper studies model selection for general unit-root time series, including the case with many exogenous predictors. We propose a new model selection algorithm, FHTD, that leverages forward stepwise regression (FSR), a high-dimensional information criterion (HDIC), a backward elimination method based on HDIC, and a data-driven thresholding (DDT) approach. Under some mild assumptions that allow for unknown locations and multiplicities of the characteristic roots on the…

时间 Wasserstein 插补：一种灵活的时间序列缺失值方法AI 解读

Missing data can significantly hamper standard time series analysis, yet they occur frequently in applications. In this paper, we introduce temporal Wasserstein imputation, a novel method for imputing missing data in time series. Unlike most existing techniques, our approach is fully nonparametric, circumventing the need for model specification prior to imputation, making it suitable for empirical applications even with nonlinear dynamics. Its principled algorithmic…

使用大量预测变量的时间序列预测AI 解读

We propose a novel approach for time series forecasting with many predictors, referred to as the GO-sdPCA, in this paper. The approach employs a variable selection method known as the group orthogonal greedy algorithm and the high-dimensional Akaike information criterion to mitigate the impact of irrelevant predictors. Moreover, a novel technique, called peeling, is used to boost the variable selection procedure so that many factor-relevant predictors can be included in…