Tail-Dependent Price Escalation Risk in Road Projects: A Hybrid LSTM-Gumbel Copula Model for Probabilistic Contingency Estimation

Abstract Road and bridge projects are exposed to escalation in key construction inputs such as diesel, cement, structural steel, and construction steel, where common shocks can generate jointly adverse price movements and weaken fixed-percentage contingency practices. Prior construction cost-forecasting studies have largely emphasized single-series point accuracy and often rely on independence or linear dependence assumptions, leaving a gap in contingency sizing that explicitly accounts for multivariate co-movement in escalation shocks. This study proposes a hybrid framework that couples multivariate long short-term memory (LSTM) forecasting of monthly input-index log-returns with copula-based dependence modeling of strictly out-of-sample forecast innovations. The workflow follows a blocked walk-forward design, using separate validation and test blocks for dependence calibration and final evaluation, respectively. A Monte Carlo engine integrates the trend component and dependent residual shocks to generate joint escalation scenarios and produce decision-grade cost percentiles. Using official Peruvian monthly indices from 2013 to 2025, the empirical results show heterogeneous dependence across inputs, with the strongest positive rank association observed between structural steel and construction steel ( τ = 0.9394 ), while several other pairwise links are weak or negative. In this context, the Gumbel copula is used as a conservative upper-tail benchmark, yielding θ ˆ = 16.5000 and λ ˆ U = 0.9571 . For the analyzed material basket, the benchmark tail-dependent model yields contingency requirements of 1.72% at the 90% confidence level and 3.99% at the 95% level above 50th percentile ( P 50 ). The results show that dependence assumptions materially affect high-confidence cost thresholds and that contingency reserves are better treated as confidence-based governance choices than as fixed deterministic add-ons.