Assessment of Non-Linear Lag Effects of Drought on Sectoral Stock Returns Using a Histogram Gradient Boosting Autoregressive Approach

Drought is a slow-onset hazard whose economic impacts can propagate across sectors with multi-year delays. This study develops a non-linear autoregressive model with exogenous drought inputs (ARX) to assess whether U.S. drought severity, measured by the Drought Severity and Coverage Index (DSCI), contains incremental predictive information for monthly stock returns. Using weekly DSCI and stock price data from 2013 to 2023, we constructed monthly compound returns and multi-year drought lags spanning 1–5 years for four sector-representative firms: a water utility (American Water Works, AWK), two food service firms (Chipotle Mexican Grill, CMG; Starbucks, SBUX), and an industrial manufacturer (Tesla, TSLA). We compared regularized linear ARX baselines (Elastic Net, Ridge) with a non-linear Histogram Gradient Boosting Regressor (HGB) ARX model and used permutation importance to diagnose drought-relevant lag horizons. Results showed a clear, delayed drought signal for the water utility, with a dominant ~48-month drought lag, consistent with multi-year transmission through operations, regulation, and investment cycles. In contrast, drought lags added limited or unstable information for the food service firms and negligible information for TSLA, whose dynamics were dominated by non-drought drivers. Overall, the findings indicate that drought–return relationships are sector-specific and can emerge at multi-year lags, and that non-linear ARX models provide a flexible tool for detecting these delayed climate-risk signals.