In the statistical analysis of functional brain imaging data, regression analysis and cross correlation analysis between time series data on each grid point have been widely used. The results can be graphically represented as an activation map on an anatomical image, but only activation signal, whose temporal pattern resembles the predefined reference function, can be detected. In the present study, we propose a fusion method comprising innovation approach in time series analysis and statistical test. Autoregressive (AR) models were fitted to time series data of each pixel for the range sufficiently before or after the state transition. Then, the remaining time series data were filtered using these AR parameters to obtain its innovation (filter output). The proposed method could extract brain neural activation as a phase transition of dynamics in the system without employing external information such as the reference function. The activation could be detected as temporal transitions of statistical test values. We evaluated this method by applying to optical imaging data obtained from the mammalian brain and the cardiac sino-atrial node (SAN), and demonstrated that our method can precisely detect spatio-temporal activation profiles in the brain or SAN.