Complexity and scaling descriptors as diagnostic predictors of heliophysical indices across solar-cycle timescales

Heliophysical variability emerges from a coupled, multiscale system in which changes in the solar atmosphere and heliospheric plasma translate into measurable signatures in widely used activity indices. Operational space-weather workflows often summarize this variability through amplitudes and a small set of bulk solar-wind covariates, yet important dynamical information may also reside in the evolving morphology of the signals. We examine whether shape descriptors computed from heliophysical time series provide information beyond classical amplitude summaries and standard bulk solar-wind covariates. Using daily OMNIWeb-era records spanning 1964–2025, we compute ten sliding-window descriptors under a past-only convention, designed to capture complementary aspects of temporal morphology such as irregularity, roughness, and long-range dependence. The descriptor set combines entropy measures, fractal-dimension estimators, the Hurst exponent, and Lempel–Ziv (LZ) complexity, yielding a compact representation of time-series structure that is not reducible to amplitude alone. The window length is treated as a methodological hyperparameter and selected through a target-specific sensitivity analysis that jointly favors competitive out-of-sample RMSE and stable permutation-importance rankings across neighboring windows. Two complementary learners, gradient boosting and a multilayer perceptron, are used as diagnostic probes to quantify permutation-based feature relevance under chronological splitting and training-only preprocessing. Across three targets (F10.7, Sunspot Number, and Dst), shape descriptors consistently rank among the most informative predictors, often matching or exceeding the relevance of standard solar-wind inputs. The most robust signals arise from LZ complexity and a compact subset of entropy/fractal measures, whose windowed trajectories track solar-cycle phases with characteristic lead–lag behaviour. Correlation analyses on both levels and standardised first differences expose redundancy within descriptor families and reduce spurious associations driven by shared nonstationarity, motivating a family-level interpretation of relevance rather than causal attribution. Overall, the results indicate that heliophysical time-series morphology encodes dynamical information complementary to amplitude- and bulk-plasma descriptions, suggesting compact, instrument-light features for augmenting future space-weather modelling pipelines.