Trend and Fractality Assessment of Mexico's Stock Exchange

TL;DR

This study analyzes 23 years of Mexico's stock exchange data using fractality and trend assessment techniques, revealing long-range memory effects and power-law decay in returns, aiding better market prediction.

Contribution

It applies fractality and trend analysis methods to Mexican stock data, uncovering long-term dependencies and statistical properties of returns not previously detailed.

Findings

Presence of long-range memory effects in stock prices

Returns follow a Markovian random walk with alpha-stable steps

Returns decay as a power law with exponent around 2.5

Abstract

The total value of domestic market capitalization of the Mexican Stock Exchange was calculated at 520 billion of dollars by the end of November 2013. To manage this system and make optimum capital investments, its dynamics needs to be predicted. However, randomness within the stock indexes makes forecasting a difficult task. To address this issue, in this work, trends and fractality were studied using GNU-R over the opening and closing prices indexes over the past 23 years. Returns, Kernel density estimation, autocorrelation function and R/S analysis and the Hurst exponent were used in this research. As a result, it was found that the Kernel estimation density and the autocorrelation function shown the presence of long-range memory effects. In a first approximation, the returns of closing prices seems to behave according to a Markovian random walk with a length of step size given by an alpha-stable random process. For extreme values, returns decay asymptotically as a power law with a characteristic exponent approximately equal to 2.5.