Dependence-Aware Lag-Resolved Correlation Analysis in Multi-Sensor Stochastic Systems

Exploratory lag-resolved correlation analysis is widely used when potential dependence between concurrently recorded signals may be delayed, transient, or weak. In autocorrelated time series, however, scanning across candidate lags creates a multiple-comparison problem, while temporal dependence invalidates naive permutation or parametric correlation tests. This paper presents a practical dependence-aware scan-level inference procedure for exploratory lag-resolved correlation analysis under temporal autocorrelation. The procedure combines baseline standardisation, lag-resolved Pearson correlation, dependence-preserving surrogate construction (here implemented using block permutation), and max-statistic correction so that inference is performed on the largest absolute correlation observed across the scanned lag domain rather than on post hoc selected lags. The contribution is integrative rather than metric-driven: established components are assembled into a fixed, auditable inference pipeline that preserves within-channel temporal structure while controlling familywise error across exploratory lag scans. The procedure is intended for multi-sensor stochastic systems in which weak synchrony must be distinguished from artefacts of temporal dependence and analytical flexibility. Synthetic null simulations illustrate false-positive inflation under naive lag scanning, characterise calibration through a block length sensitivity analysis, and compare complete inference pipelines, demonstrating that, under the dependence regimes examined here, valid exploratory lag inference requires scan-level multiplicity control in addition to dependence-preserving surrogate generation.