Multi-scale coherence and linear system forecasting based on high-frequency data in the futures market

This study develops a multi-scale analytical framework to characterize the time–frequency co-movement and predictability of cross-contract prices in China’s futures market. Using minute-level data from 55 futures contracts (2012–2022), it integrates time-domain cross-correlation with frequency-domain techniques — such as fast Fourier transform (FFT), coherence spectrum and spectral transfer functions — to reveal lagged dependencies and frequency-specific linkages. Empirical findings show that while contemporaneous correlations are generally weak, strong coupling emerges at low frequencies when time lags are introduced, reflecting the transmission of macroeconomic signals. Structurally similar pairs, such as 5-year and 2-year treasury futures (TF–TS), maintain stable coherence and spectral response across all frequencies, whereas dissimilar pairs, such as live hog and urea futures (LH–UR), show limited low-frequency coupling with rapid high-frequency decay. A spectral filtering-based forecasting model is proposed, which performs well for tightly coupled contracts (TF [Formula: see text] TS, [Formula: see text]) but poorly for heterogeneous ones (UR [Formula: see text] LH, [Formula: see text]). The results underscore the importance of structural similarity for effective frequency-domain forecasting and offer a novel framework for modeling multi-scale interdependencies in futures markets.