High-Dimensional Knockoffs Inference for Time Series Data

TL;DR

This paper develops a new statistical inference method called TSKI for high-dimensional time series data, addressing serial dependence and unknown covariate distributions to control false discovery rate.

Contribution

It introduces TSKI, combining subsampling and e-values, extending robust knockoffs to time series, and provides theoretical guarantees for FDR control under dependence.

Findings

TSKI achieves asymptotic FDR control under certain conditions.

Power analysis shows effectiveness of TSKI with Lasso statistics.

Simulation and economic data demonstrate practical applicability.

Abstract

We make some initial attempt to establish the theoretical and methodological foundation for the model-X knockoffs inference for time series data. We suggest the method of time series knockoffs inference (TSKI) by exploiting the ideas of subsampling and e-values to address the difficulty caused by the serial dependence. We also generalize the robust knockoffs inference in Barber, Cand\`es, and Samworth to the time series setting to relax the assumption of known covariate distribution required by model-X knockoffs, since such an assumption is overly stringent for time series data. We establish sufficient conditions under which TSKI achieves the asymptotic false discovery rate (FDR) control. Our technical analysis reveals the effects of serial dependence and unknown covariate distribution on the FDR control. We conduct a power analysis of TSKI using the Lasso coefficient difference knockoff statistic under the generalized linear time series models. The finite-sample performance of TSKI is illustrated with several simulation examples and an economic inflation study.