Quantile Autoregressive Distributed Lag Unit Root Test // Implements the Quantile Autoregressive Distributed Lag (QADF) unit root test proposed by Koenker and Xiao (2004) doi:10.1198/016214504000001114. The test examines unit root behaviour across the conditional distribution of a time series using quantile regression, providing a richer characterisation of persistence than standard ADF tests. Critical values follow Hansen (1995) doi:10.1017/S0266466600009713. Lag order selection is supported via AIC, BIC, or the t-statistic sequential testing approach.