This paper presents a method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured by functional magnetic resonance imaging (fMRI). The method involves convolving the sensory input with an estimate of the hemodynamic response function, which is derived from intrinsic autocorrelations in the physiological data. This approach is validated within the framework of statistical parametric mapping (SPM) by using a measure of cross-correlations that accounts for intrinsic autocorrelations. The key aspects of the method include: 1. **Hemodynamic Response Function**: The hemodynamic response function is assumed to be Poisson-distributed and estimated from intrinsic autocorrelations. This function models the delay and dispersion of the hemodynamic response to sensory input. 2. **Statistical Parametric Mapping (SPM)**: SPMs are used to threshold the data to identify significant correlations. The statistic ζ(0) is defined as the correlation between the convolved sensory input and hemodynamic response, scaled by the square root of the effective degrees of freedom ν. 3. **Thresholding**: The threshold for significance is chosen to ensure that the probability of identifying a significant region by chance is small (e.g., 0.05). This is achieved by considering the spatial autocorrelations in the SPM and using established thresholding techniques. 4. **Validation**: The method is validated using both simulated and real fMRI data. The simulated data show good agreement with the theoretical distributions, and the real data demonstrate the specificity and robustness of the approach. 5. **Discussion**: The proposed method provides a reasonable characterization of fMRI time-series and is robust as long as the delay and dispersion parameters are within a reasonable range. The approach is unbiased and does not rely on any assumed input, making it a reliable tool for detecting significant correlations between sensory input and the brain's physiological response.This paper presents a method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured by functional magnetic resonance imaging (fMRI). The method involves convolving the sensory input with an estimate of the hemodynamic response function, which is derived from intrinsic autocorrelations in the physiological data. This approach is validated within the framework of statistical parametric mapping (SPM) by using a measure of cross-correlations that accounts for intrinsic autocorrelations. The key aspects of the method include: 1. **Hemodynamic Response Function**: The hemodynamic response function is assumed to be Poisson-distributed and estimated from intrinsic autocorrelations. This function models the delay and dispersion of the hemodynamic response to sensory input. 2. **Statistical Parametric Mapping (SPM)**: SPMs are used to threshold the data to identify significant correlations. The statistic ζ(0) is defined as the correlation between the convolved sensory input and hemodynamic response, scaled by the square root of the effective degrees of freedom ν. 3. **Thresholding**: The threshold for significance is chosen to ensure that the probability of identifying a significant region by chance is small (e.g., 0.05). This is achieved by considering the spatial autocorrelations in the SPM and using established thresholding techniques. 4. **Validation**: The method is validated using both simulated and real fMRI data. The simulated data show good agreement with the theoretical distributions, and the real data demonstrate the specificity and robustness of the approach. 5. **Discussion**: The proposed method provides a reasonable characterization of fMRI time-series and is robust as long as the delay and dispersion parameters are within a reasonable range. The approach is unbiased and does not rely on any assumed input, making it a reliable tool for detecting significant correlations between sensory input and the brain's physiological response.