The Theil index is much used in economy and finance; it looks like theShannon entropy, but pertains to event values rather than to theirprobabilities. Any time series can be remapped through the Theil index.Correlation coefficients can be evaluated between the new time series, therebyallowing to study their mutual statistical distance, - to be contrasted to theusual correlation distance measure for the primary time series. As an examplethis entropy-like correlation distance method (ECDM) is applied to the GrossDomestic Product of 20 rich countries in order to test some economyglobalization process. Hierarchical distances allow to construct (i) a linearnetwork, (ii) a Locally Minimal Spanning Tree. The role of time averaging infinite size windows is illustrated and discussed. It is also shown that themean distance between the most developed countries, was decreasing since 1960till 2000, - which we consider to be a proof of globalization of the economyfor these countries.
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