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

2025/09/26 by Dijk, Dylan, Cho, Haeran
#FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2509.22235

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 ε∈ (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.

Citations

• Factor Models With Sparse Vector Autoregressive Idiosyncratic Components
• Data-Driven Tuning Parameter Selection for High-Dimensional Vector Autoregressions
• Huber Principal Component Analysis for Large-dimensional Factor Models
• Are Latent Factor Regression and Sparse Regression Adequate?
• Rate-Optimal Robust Estimation of High-Dimensional Vector Autoregressive Models
• Bridging factor and sparse models
• Quantile factor analysis for large-dimensional time series with statistical guarantee
• Estimating Number of Factors by Adjusted Eigenvalues Thresholding
• Large-dimensional Factor Analysis without Moment Constraints
• Probability inequalities for high dimensional time series under a triangular array framework
• Factor-Adjusted Regularized Model Selection
• A Shrinkage Principle for Heavy-Tailed Data: High-Dimensional Robust Low-Rank Matrix Recovery
• A useful variant of the Davis--Kahan theorem for statisticians
• Regularized estimation in sparse high-dimensional time series models
• A Direct Estimation of High Dimensional Stationary Vector Autoregressions
• Large Covariance Estimation by Thresholding Principal Orthogonal\n Complements
• Improved penalization for determining the number of factors in approximate factor models
• Forecast comparisons in unstable environments
• Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets
• The Generalized Dynamic-Factor Model: Identification and Estimation
• Estimating the Dimension of a Model

Related

• Tail-robust factor modelling of vector and tensor time series in high dimensions
• Robust Estimation of Sparse, High Dimensional Time Series with Polynomial Tails
• Rate-Optimal Robust Estimation of High-Dimensional Vector Autoregressive Models
• A Direct Estimation of High Dimensional Stationary Vector Autoregressions
• High-Dimensional Vector Autoregression with Common Response and Predictor Factors