Scientific progress in information theory quantifiers

The Bandt and Pompe method (BPM) has been successfully applied to estimate the information theory quantifiers. The most significant limitation of the BPM is that this approach is based on point estimation. This research provides scientific progress into the several applications of the information theory quantifiers. In this way, we propose a new statistic confidence interval estimation method for the Permutation Entropy, Fisher Information Measure, and Macroeconophysics Indicator of Efficiency (MIEE). Therefore, we examine quarterly Gross Domestic Product (GDP) time series for 25 countries members of the Organization for Economic Co-operation and Development (OECD). The periods cover more than 59 years, from Q1-1960 to Q3-2019, with 238 data points. For each GDP time series, we employ the non-parametric method Local Block Bootstrap to provide a stylized fact about an empirical distribution for these data taking into account the information theory quantifiers. Based on the values of the empirical distribution of the information theory quantifiers, we construct the Shannon-Fisher causality plane (SFCP), which allows us to quantify the disorder and evaluate randomness present in the time series of quarterly GDP in each country. In addition, we use information theory quantifiers to rank the most efficient countries in allocating the resources arising from economic growth to generate a virtuous cycle of growth. Also, we apply the Principal Component Analysis (PCA) to check the results of the empirical distribution of the MIEE. We find the PCA promotes the same result as the MIEE. Our results suggest an alternative form of clustering using information theory quantifiers linked to the similarity of countries’ GDPs and the mutual influences of one country’s economic growth on the others.