2013 Volume 19 Issue 1 Pages 35-41
Time series in physical and information sciences often show nonstationary trends and are beyond the scope of the conventional methods under assumption of stationarity. Especially, if infinitely many possible trends can occur unpredictably, it is difficult to tackle them with a single algorithm without previous knowledge. However, it is possible to estimate interesting statistical parameters from the data with unpredictable drifts for some specific semiparametric statistical models. In this paper, with brain signals in mind we consider a semiparametric, mixture of Gaussian models where the trend distribution is not restricted at all. We derive an estimator of the covariance matrix for multivariate time series and demonstrate that it works robustly against any unpredictable temporal drift in signals (means) while the conventional cross-correlogram leads to spurious correlations contaminated by the drift.
