A new discrete economic model involving generalized fractal derivative

The current article is mainly concerned with applying generalized fractal derivatives in a macroeconomic model. We propose a discrete model involving four macroeconomic variables, the gross domestic production, exchange rate, money supply and exports/imports by using the generalized fractal derivative. The fractal derivative can describe the power-law phenomenon and memory property of economic variables more accurately. Based on the concrete macroeconomic data of Canada, the coefficients of this nonlinear system are estimated by the method of least squares. The statistical test results show that the four variables we have selected have an apparent causal connection, and the sum of squared residuals of the fitting equations is also acceptable. In simulation, the actual data of Canada from 1990 to 2008 are considered, and the effectiveness of our model is verified. The empirical study shows that in the coming few years, the money supply will grow quickly and hence it may lead to proper inflation.