This paper presents a method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured with functional magnetic resonance imaging (fMRI). The method involves testing for correlations between sensory input and the hemodynamic response after convolving the sensory input with an estimate of the hemodynamic response function. This estimate is obtained without reference to any assumed input. To lend the approach statistical validity, it is brought into the framework of statistical parametric mapping (SPM) by using a measure of cross-correlations between sensory input and hemodynamic response that is valid in the presence of intrinsic autocorrelations. These autocorrelations are necessarily present due to the hemodynamic response function or temporal point spread function. Two fundamental aspects of MRI data that bear directly on detecting significant correlations are the transient nature of the hemodynamic response and the inherent autocorrelation due to the sampling interval of MRI techniques. The hemodynamic response is transient, delayed, and dispersed in time. Due to the short sampling interval of some MRI techniques, the resulting time-series can show substantial autocorrelation. The transient nature of the hemodynamic response is usually attributed to a physiological uncoupling of regional cerebral perfusion and oxygen metabolism. The result is a time-dependent change in the relative amounts of venous oxy- and deoxy-hemoglobin. This change subtends the measured signal. The physiological mechanisms that mediate between neuronal activity and physiology at the level of perfusion and cerebral metabolism have time-constants in the millisecond to seconds range. The hemodynamic response function can be thought of as a temporal point spread function that not only smooths sensory input but also applies a shift in time. To assess the true "correlation" between a sensory parameter and hemodynamic response, the sensory parameter must first be subject to the same delay and dispersion as that mediating between neuronal activity and hemodynamics. The correlation of interest is between the MRI time-series and the sensory input convolved with the hemodynamic response function. The stationariness of the intrinsic autocorrelations (and implicitly the response function) referred to above are in time. Stationariness in time does not imply stationariness in space. In other words, it is possible for the response function and the autocorrelative behavior of hemodynamics to vary from region to region, or voxel to voxel. The relationship between intrinsic autocorrelations (both spatial and temporal) and the effective degrees of freedom is a general one and affects the analysis of all functional imaging data, using any form of statistical parametric mapping. In what follows, this theme occurs twice—in deriving a statistical quotient, which tests for significant temporal cross-correlations in the presence of intrinsic autocorrelations; and thresholding the resulting statistical parametric maps, which are spatially autocorrelated. The paper presents the theoretical aspects of assessing the significance of correlations between sensory (cognitive or motor) parameters and hemodynamic responses measured with MRI, an application to real data,This paper presents a method for detecting significant and regionally specific correlations between sensory input and the brain's physiological response, as measured with functional magnetic resonance imaging (fMRI). The method involves testing for correlations between sensory input and the hemodynamic response after convolving the sensory input with an estimate of the hemodynamic response function. This estimate is obtained without reference to any assumed input. To lend the approach statistical validity, it is brought into the framework of statistical parametric mapping (SPM) by using a measure of cross-correlations between sensory input and hemodynamic response that is valid in the presence of intrinsic autocorrelations. These autocorrelations are necessarily present due to the hemodynamic response function or temporal point spread function. Two fundamental aspects of MRI data that bear directly on detecting significant correlations are the transient nature of the hemodynamic response and the inherent autocorrelation due to the sampling interval of MRI techniques. The hemodynamic response is transient, delayed, and dispersed in time. Due to the short sampling interval of some MRI techniques, the resulting time-series can show substantial autocorrelation. The transient nature of the hemodynamic response is usually attributed to a physiological uncoupling of regional cerebral perfusion and oxygen metabolism. The result is a time-dependent change in the relative amounts of venous oxy- and deoxy-hemoglobin. This change subtends the measured signal. The physiological mechanisms that mediate between neuronal activity and physiology at the level of perfusion and cerebral metabolism have time-constants in the millisecond to seconds range. The hemodynamic response function can be thought of as a temporal point spread function that not only smooths sensory input but also applies a shift in time. To assess the true "correlation" between a sensory parameter and hemodynamic response, the sensory parameter must first be subject to the same delay and dispersion as that mediating between neuronal activity and hemodynamics. The correlation of interest is between the MRI time-series and the sensory input convolved with the hemodynamic response function. The stationariness of the intrinsic autocorrelations (and implicitly the response function) referred to above are in time. Stationariness in time does not imply stationariness in space. In other words, it is possible for the response function and the autocorrelative behavior of hemodynamics to vary from region to region, or voxel to voxel. The relationship between intrinsic autocorrelations (both spatial and temporal) and the effective degrees of freedom is a general one and affects the analysis of all functional imaging data, using any form of statistical parametric mapping. In what follows, this theme occurs twice—in deriving a statistical quotient, which tests for significant temporal cross-correlations in the presence of intrinsic autocorrelations; and thresholding the resulting statistical parametric maps, which are spatially autocorrelated. The paper presents the theoretical aspects of assessing the significance of correlations between sensory (cognitive or motor) parameters and hemodynamic responses measured with MRI, an application to real data,