arXiv subjects

Shuo-Chieh Huang

Publications and source records attributed to Shuo-Chieh Huang.

6 recordsLinked to original sources

arXiv2026

A Riemannian Factor Model for Manifold-Valued Time Series

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 diverge with the sample size $n$, we establish convergence rates for the estimated loading space. In particular, under short-memory and strong factor conditions, we obtain a dimension-free $n^{-1/2}$ rate, which matches the convergence rate of the high-dimensional linear factor model. Finite-sample performance of the proposed RFM is demonstrated with simulated time series on the Bures--Wasserstein manifolds and products of spheres, as well as an application to monthly realized covariances of selected U.S. stock returns---modeled as time series in the Bures--Wasserstein manifold, where the RFM provides demonstrably interpretable factors and yields competitive predictive performance.

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arXiv2026

Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions

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 feature dimension to grow polynomially with the sample size. These rates are substantially faster than the classical optimal rates for multivariate histogram density estimators that lack sparsity. Empirical evaluations show that BAND performs competitively for data sampling and confidence region forecasting against a range of state-of-the-art benchmarks.

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arXiv2026

Model Selection for Unit-root Time Series with Many Predictors

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 unit circle of the time series and conditional heteroscedasticity in the predictors and errors, we establish the sure screening property of FSR and the selection consistency of FHTD. Our theoretical analysis relies on two novel technical contributions, namely a functional central limit theorem for multivariate linear processes and a uniform lower bound for the minimum eigenvalue of the sample covariance matrices, both of which are of independent interest. Simulation results corroborate the theoretical properties and show the superior performance of FHTD in model selection. We apply the proposed FHTD to model U.S. monthly housing starts and unemployment data, showcasing its practical utility.

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arXiv2025

Temporal Wasserstein Imputation: A Versatile Method for Time Series Imputation

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 implementation can seamlessly handle univariate or multivariate time series with any non-systematic missing pattern. In addition, the plausible range and side information of the missing entries (such as box constraints) can easily be incorporated. Furthermore, our method mitigates the distributional bias common among many existing approaches, ensuring more reliable downstream statistical analysis using the imputed series. We establish the convergence of an alternating minimization algorithm to critical points. We also provide conditions under which the marginal distributions of the underlying time series can be identified. Numerical experiments, including extensive simulations covering both linear and nonlinear time series and an analysis on a real-world groundwater dataset, corroborate the practical usefulness of the proposed method.

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arXiv2024

Time Series Forecasting with Many Predictors

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 prediction. Finally, the supervised dynamic principal component analysis (sdPCA) method is adopted to account for the dynamic information in factor recovery. In simulation studies, we found that the proposed method adapts well to unknown degrees of sparsity and factor strength, which results in good performance even when the number of relevant predictors is large compared to the sample size. Applying to economic and environmental studies, the proposed method consistently performs well compared to some commonly used benchmarks in one-step-ahead out-sample forecasts.

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arXiv2024

Scalable High-Dimensional Multivariate Linear Regression for Feature-Distributed Data

Feature-distributed data, referred to data partitioned by features and stored across multiple computing nodes, are increasingly common in applications with a large number of features. This paper proposes a two-stage relaxed greedy algorithm (TSRGA) for applying multivariate linear regression to such data. The main advantage of TSRGA is that its communication complexity does not depend on the feature dimension, making it highly scalable to very large data sets. In addition, for multivariate response variables, TSRGA can be used to yield low-rank coefficient estimates. The fast convergence of TSRGA is validated by simulation experiments. Finally, we apply the proposed TSRGA in a financial application that leverages unstructured data from the 10-K reports, demonstrating its usefulness in applications with many dense large-dimensional matrices.

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