Unit Root Detection and Sensitivity to Initial Conditions in S&P/BMV IPC Index Returns

Abstract

DOI: http://doi.org/10.5281/zenodo.10541189

This study aims to address the question of whether the time series of stock returns issued by companies belonging to the FMCG sector of the S&P/BMV IPC index exhibit unit roots and sensitivity to initial conditions. This approach is based on the recognition of the importance of the presence of unit roots and initial sensitivity in financial time series. Their impact can generate significant biases in analysis, projections, decision making and risk management in stock market investments, thus affecting various economic sectors of the country. The relevance of addressing this problem lies in the need to understand how the presence of unit roots can affect market dynamics, and how sensitivity to initial conditions can play a determining role in this context. To address this research, the six issuers that make up the FMCG sector will be examined through the application of the Dickey-Fuller test and the calculation of the Lyapunov exponent. These analytical tools allowed us to evaluate the existence of unit roots and initial sensitivity in the time series of stock returns. The analysis concludes that the logarithmic return series do not need to be differentiated, since they exhibit stationarity and absence of unit roots. Using the Lyapunov exponent, negative exponents are obtained for 100% of the issuers, indicating that they have some stability and do not tend to behave chaotically.