Digital currency price prediction is vital to both sellers and purchasers. Over these years, decomposition and integration models have been applied more and more to realize the goal of precise prediction, however, many of them tend to neglect the reconstruction of features or the residual series. Altogether, one of the biggest drawbacks of the decomposition and integration framework is the method applied requires manual parameter setting whether it is for decomposition or integration. Still, for the results, they are merely satisfied with the point prediction which brings high uncertainty. In this paper, an optimized feature reconstruction decomposition and two-step nonlinear integration method is proposed which gives consideration to feature reconstruction, nonlinear integration, optimization and interval prediction. The original data series is decomposed through improved variational mode decomposition based approximate entropy feature reconstruction system. Then, improved particle swarm optimization-gated recurrent unit (iPSO-GRU) is utilized in the first and second nonlinear integration part separately. Meanwhile, the residual series is given attention, if it is not a white noise series, the residual will be the input of iPSO-GRU whose result will be added back to the second integration result to form the point prediction result. Based on the point prediction result, interval prediction estimate will be generated as well via maximum likelihood function. This study chooses three kinds of digital currency as cases and the results show that the MAPE values of point prediction are all below 3.5%, and CP values of interval prediction are all 1 with suitable MWP. In addition, compared with other benchmark models, the proposed model shows better performance.
