The objective of this paper is to develop the method of detection of the abrupt change and the trend in electroencephalographic data which is a non-stationary times series. In this paper, the Kalman filter method is applied to the detection of the abrupt change and the trend. It is shown that the detection of the abrupt change can be improved by introducing a feed-back parameter in the Kalman filter gain. For the detection of the slow changes or the trend of the time series, a spectral error measure is applied to the Kalman filter. The amplitude and the frequency changes of the time series are then extracted by the smoothing of the Kalman filter method. Numerical examples illustrate the availability of the filter and verify the methods developed here.