High-Dimensional Knockoffs Inference for Time Series Data.

Area of Science:

• Statistics
• Time Series Analysis
• Machine Learning

Background:

• Model-X knockoffs inference is a powerful tool for feature selection but faces challenges with time series data due to serial dependence.
• Existing methods often require stringent assumptions about covariate distributions, which are impractical for real-world time series.
• Addressing these limitations is crucial for reliable feature selection in dynamic systems.

Purpose of the Study:

• To establish a theoretical and methodological foundation for knockoffs inference specifically tailored for time series data.
• To develop a novel method, time series knockoffs inference (TSKI), that overcomes the limitations of existing approaches.
• To ensure robust feature selection by controlling the false discovery rate (FDR) under challenging time series conditions.

Main Methods:

• Proposed time series knockoffs inference (TSKI) by integrating subsampling and e-values to manage serial dependence.
• Generalized robust knockoffs inference to relax the assumption of known covariate distributions, making it suitable for time series.
• Established theoretical conditions for asymptotic false discovery rate (FDR) control and conducted power analysis using Lasso.

Main Results:

• Demonstrated that TSKI effectively controls the asymptotic false discovery rate (FDR) under sufficient conditions.
• Quantified the impact of serial dependence and unknown covariate distributions on FDR control through technical analysis.
• Validated the finite-sample performance of TSKI via simulations and an economic inflation study.

Conclusions:

• TSKI provides a robust and theoretically sound framework for feature selection in time series data.
• The method successfully addresses the complexities of serial dependence and unknown covariate distributions.
• TSKI offers a practical solution for reliable inference in time series analysis, as evidenced by empirical evaluations.