The current study focuses on the problem of determining investment attrаctiveness of countries by means of monitoring regional stock markets. The method of using the permutation entropy as a model of investment attractiveness estimation is suggested. We have calculated the permutation entropy for the time series of stock markets of countries for the period from 2005 to 2018. The countries with high, middle or low income in Europe, Central Asia, East Asia, the Pacific, and North America were selected for the study. The article presents the results of modeling and analysis of dynamic properties of regional stock markets using the permutation entropy. The behavior of the permutation entropy and stock markets is analyzed and conclusions about the possibility of rapid monitoring of the investment attractiveness of countries by classifying the states of the stock markets of these countries are drawn. Particular attention is paid to crisis periods. It has been shown that the permutation entropy rapidly decreases in a universal way in the pre-crisis period, which can serve as an indicator of the precursor for crisis phenomena. Determining the pre-crisis, actual crisis and post-crisis periods will allow the investor to make the right decision on time. The advantages of using the permutation entropy method as a tool for high-frequency monitoring of stock markets and modeling the investment attractiveness of countries are pointed out. The results of determining investment attractiveness in terms of the permutation entropy and ratings of the world countries, compiled by the world-wide rating agencies and literature, are compared.