The sheaf of straight lines methodology. An application to the Spanish stock market

Financial markets, and particularly stock markets, have become an essential factor in understanding the behavior of the real economies. The analysis of how the stock markets have responded to the recent financial and economic crisis is crucial to understanding the economy's behavior. However, its analysis is not an easy task due, among many other reasons, to the high number of implicated variables. Usually, different graphical techniques are applied to analyze the evolution of the stock markets and to forecast the expected trend of the quoted stock prices. This paper proposes a new graphical methodology to analyze stock market behavior: the Sheaf of Straight Lines Methodology (SoSLM). The main advantage of this methodology is that it helps to compare time paths of a set of time series for a given time period. This makes it possible to better understand the evolution of one of them with respect to the others, in relation to the formed sheaf of straight lines. Simultaneously, it eliminates the difficulties arising when a high number of time series are compared through the joined graphical representation, either in a unique chart or in separated ones. So, it is particularly suitable for application to financial markets. This paper applies the SoSLM to the 35 constituents of the Spanish IBEX 35 index from June to September of 2013. The Spanish stock market has been hit hard by the recent financial crisis, although it has shown signs of recovery since June 2013; so, it presents an interesting case for analysis.