## 6 Conclusions  
In this paper, we propose a financial time-series prediction model based on multiplexed attention and a linear transformer structure for economic time-series prediction to solve some problems of the missing historical data of traditional models and machine learning models in long time-series prediction and to improve the training rate and accuracy of financial time-series prediction in machine learning. Since the traditional transformer structure is complicated, in this paper, we simplify the transformer structure, replace the original transformer structure with the linear transformer and replace the multi-headed attention module in the encoder part of the transformer set structure with a linear Fourier transform. To make the transformer more applicable to the prediction of financial timing while retaining the multi-headed attention part in the decoder, we can improve the model's training speed and prediction accuracy based on our work. At the same time, due to the linear transformer structure, the number of operations and the number of parameters of the proposed model are reduced compared with the standard transformer model, which significantly improves the computational speed of the model. In the field of financial time-series forecasting, this occurs by specific revelation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Accuracy** & **Flops (G)** & **Parameters (M)** \\ \hline CEEMDAN [40] & 0.931 & 146.33 & 178.43 \\ \hline GNN [41] & 0.780 & 135.87 & 179.99 \\ \hline SVM [37] & 0.823 & 102.50 & 133.43 \\ \hline BP Network [39] & 0.843 & 86.34 & 137.25 \\ \hline ARIMA [38] & 0.894 & 150.66 & 178.27 \\ \hline LSTM [35] & 0.921 & 112.43 & 99.86 \\ \hline Transformer [36] & 0.940 & 160.88 & 190.54 \\ \hline
**Ours** & **0.963** & **95.32** & **91.45** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A comparison of the different models. Linear transformer models based on multi-headed attention mechanisms are highly effective in various natural language processing tasks, including language modeling, machine translation and text classification. However, they also have some limitations and potential directions for future research. One limitation of linear transformer models is that they can be computationally expensive, especially when dealing with long time-series sequences. This can slow training and inference times, which can be a problem in real-time applications. To address this, researchers are exploring ways to optimize the computation of attention weights, such as using scant attention or pruning attention heads. Another limitation is that linear transformers must be better suited for tasks requiring reasoning or inference, such as question-answering or dialogue generation. This is because they lack explicit mechanisms for representing and manipulating structured knowledge. Researchers are exploring ways to incorporate external knowledge sources, such as knowledge graphs or ontologies, into the model architecture to address this. In terms of future directions, one promising area of research is the development of hybrid models that combine the strengths of linear transformers with other neural network architectures, such as convolutional neural networks or graph neural networks. Another direction is the exploration of unsupervised pre-training techniques, such as generative pre-training or contrastive learning, to improve the efficiency and effectiveness of linear transformer models. Conceptualization, J.L. and C.X. ; methodology, B.F. and B.L. ; software, J.L., C.X. and B.F.; validation, C.X., B.F. and B.L. ; formal analysis, C.X., B.F. and B.L. ; investigation, C.X., B.F. and B.L. ; data curation, C.X. and B.F.; writing--original draft preparation, J.L., C.X. and B.L. ; writing--review and editing, J.L. and B.F.; visualization, J.L., C.X. and B.F.; supervision, J.L. ; funding acquisition, B.L. All authors have read and agreed to the published version of the manuscript. This work is supported by National Key R&D Program of China (2020 AAA0105200). Not applicable.