SICABI: Symmetry-Informed Stochastic Modeling via Dominant-Period Stationarity and Recursive Adaptive Parametric Density Estimation

Wind dynamics in urban environments exhibit non-stationarity and marked spatial variability, complicating stochastic modeling when a single global distribution is assumed. This article discusses the estimation of wind density under quasi-stationary regimes at the local level using SICABI, a two-phase framework: (i) Stationary Region Identification (ISR) estimates, through spectral power analysis, a specific dominant period for each location and validates the induced subsampling using the Augmented Dickey–Fuller (ADF) test, and (ii) RAPID adjusts an adaptive parametric density by recursively updating the mixture parameters and creating new components when a normalized membership distance exceeds a threshold. The analysis uses wind speed records collected from eight stations in the Metropolitan Area of Queretaro, Mexico, during the period from 1 January 2023 to 31 December 2023, aggregated at a 10 min resolution, from which Xδ,s is constructed for each site. RAPID is compared against Gaussian Kernel Density Estimation (KDE) with Silverman bandwidth and EM-fitted Gaussian mixtures with BIC-based selection (Kmax=12). The resulting densities were compared with an empirical density estimated from a histogram over a fixed grid (m=50) using the MISE and RMSE metrics. The results reveal marked site-dependent differences in dominant periodicity and residual behavior, including asymmetry and heavy tails. ISR identified dominant periods ranging from 37 to 166 days, and RAPID adapted its complexity with Ks∈[5,10] without fixing the number of mixture components in advance. Quantitatively, RAPID achieved the lowest RMSE at 6/8 sites and the lowest MISE at 5/8 sites, while also exhibiting shorter execution times than KDE and MoG under the same input Xδ,s. The results support RAPID as a competitive adaptive method for site-specific density estimation in non-stationary urban climate signals. In this context, local regimes can be viewed as approximate invariants under time translation in the weak stochastic sense, while deviations from this assumption are reflected in increased distributional complexity across sites.