The Journal of Grey System ›› 2026, Vol. 38 ›› Issue (4): 38-50.

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Prediction and Analysis of Trade Index between China and the Countries of Belt and Road Partner with an Improved Grey Model

  

  1. 1. School of Business, Chongqing City Management Vocational University, Chongqing, 401331, P.R. China
    2. School of Mathematical Statistics, Chongqing Technology and Business University, Chongqing, 400067, P.R. China
  • Online:2026-09-25 Published:2026-09-25

Abstract:

The Trade Index published by the General Administration of Customs of China is an important composite indicator for tracking trade dynamics under the Belt and Road Initiative (BRI). However, the annual series is short and exhibits considerable uncertainty and structural variation, which limits the applicability of data-intensive forecasting methods. To address this issue, this study develops a dual-parameter-optimized DGM(1,1,r,ξ) grey prediction model by jointly estimating the fractional accumulation order r and the background-value coefficient ξ. Using annual Trade Index data for China and Belt and Road partner countries from 2013 to 2023, the empirical results show that the proposed PSO-optimized DGM(1,1,r,ξ) model achieves the lowest comprehensive percentage error (0.91%) among the competing grey models. Compared with the single-parameter DGM(1,1,r) model, the improvement is slight, but the proposed model still provides the best overall balance between in-sample fitting and out-of-sample prediction under the unified evaluation framework. These results suggest that the joint optimization of r and ξ can improve predictive performance in a small-sample and policy-sensitive setting. This study provides an empirically grounded grey modelling framework for Trade Index forecasting and a quantitative reference for analyzing trade dynamics under uncertainty.