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Long-range temporal interactions of brain functional magnetic resonance imaging (fMRI) signals offer a noninvasive window into human excitation-inhibition balance (EIB). We evaluated four Hurst exponent (H) estimation methods: continuous wavelet transform (CWT), discrete wavelet transform (DWT), detrended fluctuation analysis (DFA), and fractionally integrated noise (FIN) modeling. Validation first employed simulated fractional Gaussian noise and fractional Brownian motion signals of varying timeseries lengths, then phantom data to assess robustness to scanner noise. Restingstate fMRI and spectroscopy (MRS) data from 36 healthy participants enabled in-vivo validation by correlating H with biologicallyrelevant MRS-derived EIB in the left dorsolateral prefrontal cortex. Estimation accuracy improved with longer series, and for short signals, DFA and FIN performed best. Phantom and in-vivo results demonstrate consistent, reproducible H estimation across methods. Crucially, H correlated negatively with EIB, supporting H as a meaningful noninvasive biomarker for EIB in cognitive and clinical neuroscience.