Bootstrap-Based Imputation of Monthly Hydroclimatic Series Using STL Decomposition, ARFIMA/ARIMAX Modeling, and ENSO Stratification

Abstract

Background

Hydroclimatic time series with missing records compromise trend detection, hydrological modelling, and water resources management. Existing imputation methods rarely integrate seasonal decomposition, long-memory stochastic modelling, multivariate dependence, ENSO-driven nonstationarity, and uncertainty quantification within a single reproducible pipeline.

Methods

ACEBoot v1.0.0, a six-module bootstrap-based multimethod framework for monthly hydroclimatic imputation, is presented. The pipeline combines: (M1) stationarity and long-memory diagnosis via ADF, KPSS, Phillips–Perron and DF-GLS tests plus Geweke–Porter-Hudak fractional differencing; (M2) robust STL seasonal decomposition; (M3) ARFIMA or ARIMAX-ONI modelling with Gaussian copula over residuals and Moving Block Bootstrap (MBB) uncertainty propagation; (M4) structural break detection via a unified Worsley–Strucchange–ENSO filter; (M5) targeted re-imputation over confirmed break segments; and (M6) hold-out cross-validation with IC95 coverage, RMSE, MAE, ACF error and Lilliefors normality diagnostics. The framework is demonstrated on a 46-year (1977–2022) monthly streamflow series (405 observed, 147 missing; 26.6%) from the Jamundí-Carretera gauge (code 2622100403, CVC monitoring network), Río Jamundí sub-basin (sub-zone 2629), Cauca Hydrographic Zone (ZH-26), Valle del Cauca, Colombia.

Key Results

The ARIMAX-ONI(3,1,2) model, selected after majority-vote stationarity assessment (ntrain = 324, Precision profile, CV = 20%) and long-memory detection (d = 0.311, H = 0.811), achieves IC95 empirical coverage of 93.83% (nominal 95%), ACF preservation error of 0.0028, bias of 0.37 m³/s (1.0% of mean), and Lilliefors p = 0.0978. A structural break at February 1995 (+41.7% mean shift, validated by El Niño ONI = 0.72) is detected by Strucchange and confirmed by ENSO stratification. The imputed series preserves mean (+0.4%) while exhibiting expected variance reduction (−22.5%) attributable to conditional mean imputation.

Conclusions

ACEBoot v1.0.0 produces statistically valid imputations for monthly hydroclimatic series with complex missing-data patterns, integrating climate covariate information and structural break correction within a fully reproducible open-source framework. The framework is recommended for monthly streamflow series ≥20 years with ENSO influence, non-random missing-data patterns, and potential structural breaks. The open-source R implementation and interactive Spanish-localized Shiny application facilitate operational deployment in regional hydrological agencies across Spain and Latin America.