Permutation entropy and statistical analysis of the historical evolution of the Mexican stock market index

The objective of this work is to analyze the Indice de Precios y Cotizaciones (IPC), which is the Mexican stock market index, by using several statistical tools in order to study the tendencies that can shed light on the evolution of the IPC towards a more efficient market. The methodology used is to apply the statistical tools to the Mexican index and compare the results with a mature and well-known market index such as the Dow Jones Industrial Average (DJIA). We employ an autocorrelation analysis, and the volatility of the indexes, applied to the daily returns of the closing price on a moving time window during the studied period (1980-2018). Additionally, we perform an order three permutation entropy analysis, which can quantify the disorder present in the time series. Our results show that there is evidence that the IPC has become more mature since its creation and that it can be considered an efficient market since around year 2000. The behavior of the several techniques used shows a similar behavior to the DJIA which is not observed before that year. There are some limitations mainly because there is no high frequency data that would permit a more detailed analysis, specifically in the periods before and after a crisis is located. Our conclusion is that since around the year 2000, the Mexican stock index displays the typical behavior of other mature markets and can be considered as one.