Time series analysis of brain potentials preceding voluntary movements

Brain potentials preceding voluntary movements, obtained after averaging single-trial EEG records synchronised with the start of movement, consist of slow potentials shifts SPS in the negative direction mixed with faster components like ongoing EEG activity. Two hypotheses were tested: SPS could be presented by a sum of smooth function (trends) and weakly stationary processes (residuals); the residuals and the ongoing EEG activity preceding SPS could be described by the same class of autoregressive (AR) or autoregressive moving average (ARMA) models. The trend was estimated by comparing several approximating functions in the sense of least mean square error. The SPS residuals, after subtracting the trend and background EEG activity, were estimated using AR and ARMA models of different orders. These procedures were performed on brain potentials recorded from vertex to linked ear lobes of five subjects instructed to voluntarily press a button. As a result, the hypotheses were not rejected. The trend was best approximated by a hyperbolic function or Chebyshev's second order polynomial. AR models fitted both the SPS residuals and ongoing EEG activity well enough. In conclusion, SPS were characterised by three parameters of the smooth function plus a time parameter defined by the potential boundaries.