Introducing fuzzy based interaction systems for prediction of multivariate time series

In this paper, fuzzy based interaction systems are introduced for prediction of multivariate time series. Modified interaction systems based on fuzzy denoted as FuzzIS are proposed for handling uncertainties in the observed data and more accurate prediction of the time series. Using FuzzIS, the current paper tries to study the effects of oil prices on stock market index in Iran considering the exchange rate as an exogenous variable. Four dynamical equations are utilized for modeling quantities and values of oil and stock index. IS parameters including various interactions are procured using an evolutionary optimization algorithm, imperialist colonial algorithm (ICA). The empirical investigation employs monthly time series data over the period of 1988–2012. The results show significant effects of oil revenues on stock market representing a close relationship between the two variables.