A Fourier residual modified Nash nonlinear grey Bernoulli model for forecasting the international trade of Chinese high-tech products

Although the Nash nonlinear grey Bernoulli model (NNGBM(1, 1)) is incomparable with respect to its flexibility over traditional grey models, errors are still inevitable in forecasting. The purpose of this paper is to propose a Fourier residual modified Nash nonlinear grey Bernoulli model (FNNGBM(1, 1)) and use it to forecast the nonlinear time series of the international trade of Chinese high-tech products.

A Fourier series is used to modify the forecasting residual of the NNGBM(1, 1) model, so as to improve its forecasting ability. The parameters optimization of FNNGBM(1, 1) is formulated as a combinatorial optimization problem and is solved collectively using the concept of Nash equilibrium.

The simulation and practical application to fluctuation data both prove that FNNGBM(1, 1) could offer a more precise forecast than NNGBM(1, 1) and the Fourier residual GM(1, 1) (FGM(1, 1)). The import/export data of Chinese high-tech products will maintain rapid growth, with corresponding trade balance enlargement; however, there will be a concomitant decrease in the trade specialization coefficient.

This study is deliberately general in its scope and outlook: its focus is mainly on the overall condition of Chinese high-tech products trade. Future research is recommended to analyze specific industrial trade sectors and extraneous influencing factors.

An effective method is proposed to enhance the accuracy of NNGBM(1, 1) model in forecasting a small sample, nonlinear time series.