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Multiple Testing under High-dimensional Dynamic Factor Model

Xinxin Yang, Lilun Du

TL;DR

This work tackles large-scale multiple testing in high-dimensional time series modeled by dynamic factor models with nonlinear serial dependence. It develops a scalable testing framework based on two-pass Fama–MacBeth regression combined with PCA and a chronological sample-splitting scheme that yields symmetric null test statistics via the product $T_i^{(1)}T_i^{(2)}$, enabling a data-driven FDR threshold without explicit long-run variance estimation. The authors establish a new concentration inequality for causal processes, a uniform CLT for the mean estimators, and an FDR control theorem under serial dependence, with extensions to heteroskedastic and non-sparse settings and a bias-correction variant using negative controls. Through extensive simulations and an empirical hedge-fund analysis, the proposed YD method demonstrates robust FDR control and competitive power in the presence of temporal dependence and heavy tails, outperforming several existing methods in challenging settings. The work provides a practical, theoretically sound framework for reliable large-scale inference in dynamic, high-dimensional environments.

Abstract

Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously distorts error rate control in large-scale inference. In this manuscript, we propose a new multiple testing procedure under dynamic factor models that is robust to nonlinear serial dependence. The idea is to integrate a new sample-splitting strategy based on chronological order and a two-pass Fama--Macbeth regression to form a series of test statistics with marginal symmetry properties and then to use these properties to obtain a data-driven threshold. We show that our procedure can control the false discovery rate asymptotically under high-dimensional dynamic factor models. {As a byproduct of independent interest, we establish a new exponential-type deviation inequality for the sum of random variables over various functionals of linear and nonlinear processes.} Our numerical results, including a case study on hedge fund selection, demonstrate the advantage of our proposed method over several state-of-the-art methods.

Multiple Testing under High-dimensional Dynamic Factor Model

TL;DR

This work tackles large-scale multiple testing in high-dimensional time series modeled by dynamic factor models with nonlinear serial dependence. It develops a scalable testing framework based on two-pass Fama–MacBeth regression combined with PCA and a chronological sample-splitting scheme that yields symmetric null test statistics via the product , enabling a data-driven FDR threshold without explicit long-run variance estimation. The authors establish a new concentration inequality for causal processes, a uniform CLT for the mean estimators, and an FDR control theorem under serial dependence, with extensions to heteroskedastic and non-sparse settings and a bias-correction variant using negative controls. Through extensive simulations and an empirical hedge-fund analysis, the proposed YD method demonstrates robust FDR control and competitive power in the presence of temporal dependence and heavy tails, outperforming several existing methods in challenging settings. The work provides a practical, theoretically sound framework for reliable large-scale inference in dynamic, high-dimensional environments.

Abstract

Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously distorts error rate control in large-scale inference. In this manuscript, we propose a new multiple testing procedure under dynamic factor models that is robust to nonlinear serial dependence. The idea is to integrate a new sample-splitting strategy based on chronological order and a two-pass Fama--Macbeth regression to form a series of test statistics with marginal symmetry properties and then to use these properties to obtain a data-driven threshold. We show that our procedure can control the false discovery rate asymptotically under high-dimensional dynamic factor models. {As a byproduct of independent interest, we establish a new exponential-type deviation inequality for the sum of random variables over various functionals of linear and nonlinear processes.} Our numerical results, including a case study on hedge fund selection, demonstrate the advantage of our proposed method over several state-of-the-art methods.
Paper Structure (21 sections, 4 theorems, 40 equations, 1 figure, 3 tables)

This paper contains 21 sections, 4 theorems, 40 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Dynamic Factor Models
  3. Main Results and Contributions
  4. Organization of the Paper
  5. Methodology
  6. Estimation of ${\boldsymbol{\mu}}$
  7. Multiple Testing Procedure via Sample-splitting
  8. Theoretical Results
  9. A New Concentration Inequality for Causal Processes
  10. CLT for $\widehat{\mu}_i$
  11. FDR Control Theory
  12. Extension
  13. Improvement for Heterogeneous Cases
  14. Bias Correction Using a Negative Control Set
  15. Simulation
  16. ...and 6 more sections

Key Result

Proposition 1

Suppose that $\{\varepsilon_t\}_{t\in\mathbb{Z}}$ is a sequence of i.i.d. random variables, and is a stationary process with $\mathbb{E}(X_t)=0$ and $\mathbb{E}|X_t|^d<\infty$ for some $d\geq4$. Assume that $\sup_{1\leq t\leq n}|X_t|\leq \sqrt{n}$. Then for any positive sequence $\tau_n/\log n\rightarrow\infty$ and $c_n=o(\log([\tau_n/\log n]))$, we have where $K$ is a constant that depends sole

Figures (1)

  • Figure 1: Empirical FDR and power of our method (YD), its improvement (YD$\_$R), and competitors (i.e., FARM, FAT, SBH, SN) at prespecified FDR levels $\beta=0.05, 0.1$, and $0.15$, for varying signal strengths $\nu$ when serial correlation exists and idiosyncratic errors are heterogeneous.

Theorems & Definitions (14)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Proposition 1
  • Remark 5
  • Remark 6
  • Remark 7
  • Remark 8
  • Proposition 2
  • ...and 4 more