Detection of nonlinearity and chaoticity in time series using the transportation distance function

We propose a systematic two-step framework to assess the presence of nonlinearity and chaoticity in time series. Although the basic components of this framework are from the well-known paradigm of surrogate data and the concept of short-term predictability, the newly proposed discriminating statistic, the transportation distance function offers several advantages (e.g., robustness against noise and outliers, fewer data requirements) over traditional measures of nonlinearity. The power of this framework is tested on several numerically generated series and the Santa Fe Institute competition series.