The return series of cryptocurrencies, which are emerging digital assets, exhibit nonstationarity, nonlinearity, and volatility clustering compared to other traditional financial markets, making them exceptionally difficult to forecast. Therefore, accurate cryptocurrency price forecasting is essential for market participants and regulators. It has been demonstrated that improved data forecasting accuracy can be achieved through decomposition, but few researchers have performed information extraction on the residual series generated by data decomposition. Based on the construction of a “decomposition-optimization-integration” hybrid model framework, in this paper, we propose a multi-scale hybrid forecasting model that combines the residual components after primary decomposition for secondary decomposition and integration. This model uses the variational modal decomposition (VMD) method to decompose the original return series into a finite number of components and residual terms. Then, the residual terms are decomposed, and the features are extracted using the completed ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method. The components are predicted by an extreme learning machine optimized by the sparrow search algorithm, and the final predictions are summed to obtain the final results. Forecasts for the returns of Bitcoin and Ethereum, which are significant cryptocurrency assets, are compared with other benchmark models constructed based on different ideas. We find that the proposed quadratic decomposition VMD-Res.-CEEMDAN-SSA-ELM hybrid model demonstrates the optimal and most stable forecasting performance in both one-step and multi-step ahead prediction of the cryptocurrency return series.

The regularly issued low frequency data, such as the change of fund position (weekly), and Producer Price Index (monthly), can affect the subsequent trend of stock returns. However, the forecasting effect of low frequency data on high frequency has not been discussed amply. This paper proposes a new mixed frequency neural network that helps to fill this research gap. The original time series is decomposed into several components through ensemble empirical mode decomposition, then the frequency alignment method is applied to integrate the high frequency component with low frequency variable as inputs, and the CNN-BiLSTM-Attention network completes the remaining forecasting work. The empirical results show that compared with other benchmark models, the proposed procedures perform better when predicting the high frequency components and obtain a smaller statistical error in the final ensemble results. The proposed model has great potential for the forecasting of reverse mixed time series.