Abstract
This paper establishes a model of economic growth for all the G7 countries from 1973 to 2016, in which the gross domestic product (GDP) is related to land area, arable land, population, school attendance, gross capital formation, exports of goods and services, general government, final consumer spending and broad money. The fractional-order gradient descent and integer-order gradient descent are used to estimate the model parameters to fit the GDP and forecast GDP from 2017 to 2019. The results show that the convergence rate of the fractional-order gradient descent is faster and has a better fitting accuracy and prediction effect.
Highlights
In recent years, fractional model has become a research hotspot because of its advantages
To compare the performance of fractional- and integer-order gradient descent, we visualize the rate of convergence of the cost function, evaluate the model with mean square error (MSE), mean absolute deviation (MAD) and R2 indicators and predict the gross domestic product (GDP) of the seven countries in 2017–2019 according to the trained parameters
The grid search method was used to select the appropriate learning rate and initial weight interval, and the effects of different fractional orders are compared to select the best order.The learning rate and the initial weight interval are applicable to both fractional-order gradient descent and integer-order gradient descent
Summary
Fractional model has become a research hotspot because of its advantages. The rise in fractional calculus provides a new idea for advances in the gradient descent method. Economic growth models of seven countries are established, and their cost functions are trained by gradient descent (fractional- and integer-order). To compare the performance of fractional- and integer-order gradient descent, we visualize the rate of convergence of the cost function, evaluate the model with MSE, MAD and R2 indicators and predict the GDP of the seven countries in 2017–2019 according to the trained parameters. In 1976, Canada’s accession marked the birth of the G7, whose members are the United States, the United Kingdom, France, Germany, Japan, Italy and Canada seven developed countries. Some G7 members (France, Germany, Italy and the United States) were members of the European Union (EU) during this period, so this paper establishes the economic growth model of the EU.
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