NONLINEAR FINANCIAL MODELING USING DISCRETE FRACTIONAL-ORDER DIFFERENTIATION: AN EMPIRICAL ANALYSIS

Abstract

In this study, a nonlinear financial model of economic dynamics with fractional-order derivative is proposed. Jumari type fractional-order derivative is used to make it discretization by removing the limit operation. We estimate the coefficients and parameters of the model by using least square principle. This new approach to financial system modelling is illustrated by an application to model the behaviour of Indian national financial system which consists of three economic dynamics like interest rate, investment and inflation. The empirical results with different time step sizes discretization are shown; a comparison of the actual data against the data estimated by empirical model is illustrated. The comparative analysis of integer order derivative financial and the present model is shown which gives interesting facts about model. Application of fractional-order discrete technique in nonlinear financial model is a powerful tool for minimizing the error and forecasting of economic dynamics as well as for optimization of management strategy and decision technology of Indian financial system.