Introduction and application of the multiscale coefficient of variation analysis.

Quantifying how patterns of behavior relate across multiple levels of measurement typically requires long time series for reliable parameter estimation. We describe a novel analysis that estimates patterns of variability across multiple scales of analysis suitable for time series of short duration. The multiscale coefficient of variation (MSCV) measures the distance between local coefficient of variation estimates within particular time windows and the overall coefficient of variation across all time samples. We first describe the MSCV analysis and provide an example analytical protocol with corresponding MATLAB implementation and code. Next, we present a simulation study testing the new analysis using time series generated by ARFIMA models that span white noise, short-term and long-term correlations. The MSCV analysis was observed to be sensitive to specific parameters of ARFIMA models varying in the type of temporal structure and time series length. We then apply the MSCV analysis to short time series of speech phrases and musical themes to show commonalities in multiscale structure. The simulation and application studies provide evidence that the MSCV analysis can discriminate between time series varying in multiscale structure and length.