Wavelet testing for a replicate-effect within an ordered multiple-trial experiment

Experimental time series data collected across a sequence of ordered trials (replicates) often crop up in many fields, from neuroscience to circadian biology. In order to decide when to appropriately evade the simplifying assumption that all replicates stem from the same process, an assumption often untrue even when identical stimuli are applied, two novel tests are proposed that assess whether a significant trial-effect is manifest along the experiment. The modelling framework uses wavelet multiscale constructions that mitigate against the potential nonstationarities often present in experimental data, both across times and across replicates. The proposed tests are evaluated in thorough simulation studies and illustrated on neuroscience data, proving to be flexible tools with great promise in dealing with complex multiple-trials time series data and allowing the analyst to accordingly tune their subsequent analysis.