Tail-robust estimation of factor-adjusted vector autoregressive models for high-dimensional time series

2025-09-26

AI Summary

This paper addresses the challenge of modeling high-dimensional heavy-tailed time series. We propose the Factor-Adjusted Sparse Vector Autoregression (FAR-VAR) model, which captures pervasive co-movements among variables via a low-rank common factor structure and models residual dynamic dependencies through a sparse VAR component. Methodologically, under a weak moment condition requiring only (2+2ε)-th order finite moments, we develop a two-stage robust estimation procedure: element-wise truncation preprocessing, principal component analysis for latent factor estimation, and Lasso-type penalized estimation for the sparse coefficient matrix. Theoretically, we establish the first explicit characterization of how the tail heaviness affects estimation convergence rates and derive verifiable error bounds. Simulation studies and macroeconomic empirical analysis demonstrate that FAR-VAR significantly outperforms conventional Gaussian-based VAR and factor models under heavy-tailed settings, achieving both statistical robustness and superior forecasting performance.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Time-Series/Data Streams

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as well as their remaining interconnectedness using a sparse VAR model. To accommodate heavy tails, we adopt an element-wise truncation step followed by a two-stage estimation procedure for estimating the latent factors and the VAR parameter matrices. Assuming the existence of the $(2 + 2ε)$-th moment only for some $εin (0, 1)$, we derive the rates of estimation that make explicit the effect of heavy tails through $ε$. Simulation studies and an application in macroeconomics demonstrate the competitive performance of the proposed estimators.

Problem

• Modeling high-dimensional heavy-tailed time series data
• Estimating latent factors and sparse VAR parameters robustly
• Deriving estimation rates accommodating heavy tail effects

Innovation

• Element-wise truncation for heavy-tailed data
• Two-stage estimation of factors and parameters
• Sparse VAR modeling with latent factors