Multiscale spectral modelling for nonstationary time series within an ordered multiple-trial experiment

Within the neurosciences it is natural to observe variability across time in dynamics of an underlying brain process. Wavelets are essential analysing signals because, even within a single trial, exhibit nonstationary behaviour. However, neurological generated experiment may also potentially evolution trials (replicates), for identical stimuli. As neurologists consider localised spectra be most informative, we propose MULtiple-Trials Locally Stationary Wavelet process (MULT-LSW) that fills gap literature by directly giving stochastic wavelet representation series ordered replicates itself. MULT-LSW yields desired time- and trial-localisation dynamics, capturing behaviour both trials. While current techniques restricted assumption uncorrelated replicates, here account between-trial correlation. We rigorously develop associated spectral estimation framework along with its asymptotic properties. By means thorough simulation studies, demonstrate theoretical estimator properties hold practice. A real data investigation into evolutionary hippocampus nucleus accumbens, during associative learning experiment, demonstrates applicability our proposed methodology as well new insights provides. Our model general facilitates wider experimental analysis than allows.