Why ARMAX-GARCH Linear Models Successfully Describe Complex Nonlinear Phenomena: A Possible Explanation

Economic and financial processes are complex and highly nonlinear. However, somewhat surprisingly, linear models like ARMAXGARCH often describe these processes reasonably well. In this paper, we provide a possible explanation for the empirical success of these models. 1 Formulation of the Problem Economic and financial processes are very complex. It is well know that economic and financial processes are very complex. The future values of the corresponding quantities are very difficult to predict, and many empirical dependencies are highly nonlinear. Surprising empirical success of ARMAX-GARCH models. In spite of the clearly non-linearity of the economic and financial processes, linear models are surprisingly efficient in predicting the future values of the corresponding quantities. Specifically, if we are interested in the quantity X which is affected by the external quantity d, then good predictions can often be made based on the AutoRegressive-Moving-Average model with eXogenous inputs model (ARMAX) [3, 4]: