A Novel Optimized Nonlinear Grey Bernoulli Model for Forecasting China’s GDP

Abstract

The nonlinear grey Bernoulli model, abbreviated as NGBM(1,1), has been successfully applied to control, prediction, and decision-making fields, especially in the prediction of nonlinear small sample time series. However, there are still some problems in improving the prediction accuracy of NGBM(1,1). In this paper, we propose a novel optimized nonlinear grey Bernoulli model for forecasting Chinaʼs GDP. In the new model, the structure and parameters of NGBM(1,1) are optimized simultaneously. Especially, the latest item of first-order accumulative generating operator (1-AGO) sequence is taken as the initial condition, then background value is reconstructed by optimizing weights of neighbor values in 1-AGO sequence, which is based on minimizing the sum of absolute percentage errors, and finally, we establish the new model based on the rolling mechanism. Prediction accuracy of the proposed model is investigated through some simulations and a real example application, and the proposed model is applied to forecast the annual GDP in China from 2019 to 2023.

A Rolling Optimized Nonlinear Grey Bernoulli Model RONGBM(1,1) and application in predicting total COVID-19 cases

“…Based on the simultaneous optimization of three parameters: the exponential parameter, the initial condition and the background value, we propose a further optimized algorithm of the Optimized NGBM(1, 1) given by Wu et al (2019) [41]. This algorithm is more practical and less time-consuming upon implementing in the currently available computer languages (R, Python or Matlab):…”

“…Wu et al (2019) [41] is the first paper to ever mention the application of rolling mechanism to the NGBM(1, 1) to enhance accuracy. However, the proposed model did not reach the maximum efficiency due to the following reasons:…”

“…The classification of the model precision based on ARPE is described in Table 1 below [41]. Besides ARPE, the root-mean-square error (RMSE) or root-mean-square deviation (RMSD) is also used to evaluate the precision of the model:…”

“…Notably, to reinforce the predicting accuracy, some researchers have studied and combined to create hybrid Grey models, such as grey-Markov [21,27], grey-Fourier [42], grey-Taguchi [14]. Some more hybrid models such as Grey rolling mechanism [3,7,23] or nonlinear Grey Bernoulli method [38,9,41,26] can also be taken into consideration. In this paper, rolling mechanism is combined with nonlinear Grey Bernoulli method to propose a rolling optimized nonlinear Grey Bernoulli model, or RONGBM (1,1).…”

“…The rolling mechanism implemented in Algorithm 1 of [41] is incorrect. The rolling mechanism requires the insertion of the predicted value into the new array, while removing the oldest data point.…”