Abstract
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.
Highlights
The fractal and fractional derivatives can be regarded as the generalization of usual derivatives [ – ]
5 Conclusion In this paper, we proposed a novel nonlinear discrete macroeconomic model based on the generalized fractal derivatives
One is that the generalized fractal derivative is suitable for depicting the power law in macroeconomic variables
Summary
The fractal and fractional derivatives can be regarded as the generalization of usual derivatives [ – ]. There are very few works discussing the modeling of actual macroeconomic data using discrete dynamical system. In real-world cases, many macroeconomic variables are observed sequently, i.e., daily, monthly or annually, which motivates us to construct a new model by using difference equation involving a generalized fractal derivative.
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