IPAD: Stable Interpretable Forecasting with Knockoffs Inference

TL;DR

The paper introduces IPAD, a novel stable and interpretable forecasting method using knockoffs inference that controls false discoveries in high-dimensional econometric models, with theoretical guarantees and practical effectiveness.

Contribution

IPAD is a new method that estimates covariate distributions from data, avoids sample splitting, and provides theoretical FDR control and power analysis for stable forecasting.

Findings

Demonstrates strong finite-sample performance in simulations

Achieves controlled false discovery rate in high-dimensional settings

Provides interpretable and stable forecasts in real data applications

Abstract

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped in the econometric settings. To this end, in this paper we exploit the general framework of model-X knockoffs introduced recently in Cand\`{e}s, Fan, Janson and Lv (2018), which is nonconventional for reproducible large-scale inference in that the framework is completely free of the use of p-values for significance testing, and suggest a new method of intertwined probabilistic factors decoupling (IPAD) for stable interpretable forecasting with knockoffs inference in high-dimensional models. The recipe of the method is constructing the knockoff variables by assuming a latent factor model that is exploited widely in economics and finance for the association structure of covariates. Our method and work are distinct from the existing literature in that we estimate the covariate distribution from data instead of assuming that it is known when constructing the knockoff variables, our procedure does not require any sample splitting, we provide theoretical justifications on the asymptotic false discovery rate control, and the theory for the power analysis is also established. Several simulation examples and the real data analysis further demonstrate that the newly suggested method has appealing finite-sample performance with desired interpretability and stability compared to some popularly used forecasting methods.