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Presents a new approach to the analysis of nonstationary possibly nonlinear time series. It is based on an adaptive autocorrelation eigenspectrum computation known as APEX together with a model selection rule. New concepts of stochastic instantaneous embedding dimension and time averaged instantaneous embedding dimension are introduced. The motivation for this new approach is the analysis of newborn electroencephalogram for which nonstationarity is a crucial property. Experimental data are analyzed using the proposed scheme.