FDR-Controlled Sparse Index Tracking with Autoregressive Stock Dependency Models

Maintaining false discovery rate (FDR) control is vital for reproducibility in high-dimensional variable selection applications, especially in sparse financial index tracking, where the goal is to use only a small fraction of the stocks comprising an index to design a tracking portfolio containing relevant stocks. This allows for, e.g., building a cost-efficient exchange-traded fund (ETF). Unfortunately, theoretical and experimental analyses show that dependencies among variables (i.e., stock returns) deteriorate the index tracking performance and compromise the FDR control property of existing variable selection methods such as the model-X knockoff method and the T-Rex selector. Therefore, we propose to alleviate these shortcomings by extending the flexible T-Rex framework to account for autoregressive dependency models, which are simple and yet effective models for capturing dependencies among stock returns. This allows for controlling the FDR at the investor-specified target level. Numerical experiments and a real-world sparse S&P 500 index tracking example validate our theoretical findings and show that the proposed approach controls the FDR while outperforming state-of-the-art benchmark methods in terms of detection power and index tracking performance. An implementation is available within the R package TRexSelector on CRAN.