The Input-Output Scheme to Model Financial Fluctuations in Peruvian Stock Markets

In this paper we use the well-known Input-Output scheme to model the temporal behavior of the ISBVL (ndice selectivo de la bolsa de valores de Lima) before and after the 2011 general elections in Peru. Because data exhibites abnormalities between January and July, dynamic instabilities are identified. We claim that a phase transition is manifested before and after the polls as consequence of accumulated uncertainties. Indeed, as observed on the ISBVL versus time curve, a strongly nonlinear region is identified over the time where the run-off took place. This phenomenon as reflected on the ISBVL leads to establish a phase transition from a linear to a nonlinear regime according to the behavior of the data. Furthermore, we noted that the nonlinear region is plagued by intrinsic fluctuations, noise and random events. In order to understand the phenomenology and dynamics associated a mathematical methodology in terms of convolution integrals based on input-output processes is presented. In concrete the transfer function corresponding to the nonlinear region is reconstructed. The exposed methodology in this note can be alternatively used for fitting those ISBVL curves featured by strong fluctuations and therefore to make predictions to some extent within a systematic error.