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Gross domestic product (GDP) is an important indicator to measure a country's economic development. If the future development trend of a country's GDP can be accurately predicted, it will have a positive effect on the formulation and implementation of the country's future economic development policies. In order to explore the future development trend of China's GDP, the purpose of this paper is to establish a new grey forecasting model with time power term to forecast GDP.

Firstly, the shortcomings of the traditional grey prediction model with time power term are found out through analysis, and then the generalized grey prediction model with time power term is established (abbreviated as PTGM (1,1, α) model). Secondly, the PTGM (1,1, α) model is improved by linear interpolation method, and the optimized PTGM (1,1, α) model is established (abbreviated as OPTGM (1,1, α) model), and the parameters of the OPTGM (1,1, α) model are solved by the quantum genetic algorithm. Thirdly, the advantage of the OPTGM (1,1, α) model over the traditional grey models is illustrated by two real cases. Finally the OPTGM (1,1, α) model is used to predict China's GDP from 2020 to 2029.

The OPTGM (1,1, α) model is more suitable for predicting China's GDP than other grey prediction models.

A new grey prediction model with time power term is proposed.