Finite Temporal Correlation Scale in GNSS Satellite Clock Residuals: A Comparative Test of Time-Response Models

We analyze high-rate GNSS satellite clock time series (31 GPS satellites) and report a robust correlation feature at a characteristic lag of τ ≃ 30–40 min. The signal is extracted from residual clock-bias time series obtained after subtracting a scaledependent time-response model fit (TFGR residuals). Using stacked autocorrelation functions (ACF) across satellites and phase-randomized surrogate ensembles, the peak within the target band reaches z ∼ 15–20 for multiple independent orbit/clock products (JPL and WUM). We further test whether simpler “null” explanations can reproduce the same structure. Pure-delay differencing, moving-average detrending, and AR(1)-whitening do not remove nor mimic the band-limited peak, indicating that the 30–40 min structure is not an artifact of generic low-frequency trends or short-memory stochasticity. Finally, the peak strength is approximately stable when the data are partitioned by orbital phase and by contiguous time blocks, suggesting that the effect is not confined to specific geometries or brief intervals.