Weight-calibrated estimation for factor models of high-dimensional time series

2025-05-02

AI Summary

Existing methods for high-dimensional time-series factor models impose overly restrictive assumptions—either strict white-noise errors or asymptotic identifiability—which often fail in practice. Method: We propose a novel estimation framework based on weighted calibrated autocovariance, which relaxes the white-noise assumption via a data-driven weighting scheme and integrates linear projection with low-rank vector autoregressive structure for robust latent factor extraction. Contribution/Results: Theoretically, we establish the first unified asymptotic theory comparing covariance, standard autocovariance, and weighted calibrated autocovariance estimators under varying factor strengths. Methodologically, we introduce the first weighted calibrated autocovariance estimation paradigm. Monte Carlo simulations and empirical applications to financial and macroeconomic datasets demonstrate that our approach significantly improves finite-sample estimation accuracy and robustness. Moreover, the theoretical results are both interpretable and practically applicable.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

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 performance. It adopts a linear projection to tackle high-dimensionality, and employs a reduced-rank autoregression formulation. The asymptotic theory of the proposed method is established, relaxing the assumption on white noise. Additionally, we make the first attempt in the literature by providing a systematic theoretical comparison among the covariance-based, the standard autocovariance-based, and our proposed weight-calibrated autocovariance-based methods in the presence of factors with different strengths. Extensive simulations are conducted to showcase the superior finite-sample performance of our proposed method, as well as to validate the newly established theory. The superiority of our proposal is further illustrated through the analysis of one financial and one macroeconomic data sets.

Problem

• Improves estimation in high-dimensional time series factor models
• Relaxes white noise assumption in autocovariance-based methods
• Compares covariance and autocovariance-based methods theoretically

Innovation

• Weight-calibrated method improves autocovariance-based estimation
• Linear projection tackles high-dimensionality effectively
• Reduced-rank autoregression enhances estimation performance