Tracking the Evolving Complexity of the U.S. Transportation Services Index: A Segmented Multiresolution Wavelet Entropy Analysis

Aggregate economic and infrastructural indicators often display nonlinear dynamics and structural shifts which cannot be adequately defined by conventional trend and volatility measurements. This study presents a segmented multiresolution entropy framework that blends wavelet reconstruction with Approximate Entropy (ApEn) and normalized Permutation Entropy (PE) for the evaluation of time-varying complexity. The main technique is based on applying a discrete wavelet transform with db4 to the whole series at J=3, reconstructing the low frequency component A3 and computing entropy in eight non-overlapping segments. This gives a common reconstruction basis across the sample, and it reduces sensitivity to repeated segment-boundary initialization. The framework is applied to the monthly U.S. Transportation Services Index from January 2000 to April 2026. The ApEn and PE trajectories capture changes in amplitude-based irregularity and temporal ordering consistent with periods of major economic and transportation disruption, including the global financial crisis, the COVID-19 pandemic, and subsequent supply-chain and geopolitical uncertainty. Moving-block-bootstrap intervals assess the conditional uncertainty around the main estimates. Controlled simulations demonstrate an enhanced transition-detection rate following wavelet reconstruction but not all performance criteria are improved. The results indicate that the approach can add to traditional transportation monitoring by identifying changes in system organization, independent of index level fluctuations, without suggesting causal attribution or formally validated regime shifts.