Bounds Testing for Cointegration with Many Persistent Controls

An implementation of the DML-Bounds procedure of Villena (2026) for testing cointegration in data-rich time-series settings. The Autoregressive Distributed Lag (ARDL) bounds test of Pesaran, Shin and Smith (2001) avoids pretesting the integration order of the regressors but is not designed for a high-dimensional conditioning set. Residualising the lagged levels against persistent controls can absorb stochastic trends and thereby change the finite-sample null distribution, so what governs the null is the effective number of stochastic trends surviving residualisation rather than the integration order of the original regressors. The procedure combines h-block cross-fitting, a balanced nuisance projection in the Double Machine Learning (DML) style of Chernozhukov and others (2018) , adaptive weighting after Zou (2006) , and a restricted system wild bootstrap that regenerates the dependent variable and the focal regressor jointly. No critical-value table is shipped: the classical bracket is regenerated by simulation and the operational critical value is bootstrapped. A trend-absorption diagnostic and a penalty-sensitivity sweep report whether a verdict survives a change of conditioning set. Monthly United States macroeconomic series from the 'FRED-MD' database of McCracken and Ng (2016) are bundled so every example runs offline.