Detecting Sparse Cointegration

TL;DR

This paper introduces a two-step method for detecting sparse cointegration in high-dimensional data, combining adaptive LASSO for variable selection and an information criterion for stationarity testing, with proven finite-sample robustness.

Contribution

It presents a novel approach that effectively identifies sparse cointegrating relationships and tests stationarity without relying on asymptotic assumptions.

Findings

Robust finite-sample performance demonstrated through Monte Carlo simulations

Effective variable selection in high-dimensional cointegration analysis

Reliable distinction between stationarity and nonstationarity in residuals

Abstract

We propose a two-step procedure to detect cointegration in high-dimensional settings, focusing on sparse relationships. First, we use the adaptive LASSO to identify the small subset of integrated covariates driving the equilibrium relationship with a target series, ensuring model-selection consistency. Second, we adopt an information-theoretic model choice criterion to distinguish between stationarity and nonstationarity in the resulting residuals, avoiding dependence on asymptotic distributional assumptions. Monte Carlo experiments confirm robust finite-sample performance, even under endogeneity and serial correlation.