Research on Financial Time Series Prediction Model Based on Multifractal Trend Cross Correlation Removal and Deep Learning

Due to the nonlinearity, complexity, and time-varying nature of financial data, it poses significant challenges for its prediction. With the rapid development of big data and AI technology, how to extract useful information from complex time-series data has become the key to decision-making in various industries. This article analyzes the cross correlation between Baidu Index and RMB exchange rate by applying MF-DCCA, and studies the changes in this relationship before and after the epidemic, further verifying the potential of Baidu Index in exchange rate prediction. Therefore, this article proposes an optimized deep learning model, WOA-STL-LSTM, which combines Whale Optimization Algorithm (WOA), Seasonal Trend Decomposition (STL), and Long Short Term Memory Network (LSTM). This model demonstrates superiority in predicting the Chinese yuan exchange rate. Furthermore, this article predicts the price of West Texas crude oil futures (WTI) using Google Trends data and analyzes it using LSTM. The experiment shows that Google Trends has a certain improvement effect on the prediction of WTI prices, but due to the non-linear and chaotic behavior of the time series data, the influence of Google Trends is relatively weak. Finally, this study also applied data augmentation techniques to small sample financial time series datasets, using linear interpolation and fractal interpolation methods to increase data volume. The experimental results showed that interpolated data significantly improved the accuracy of predictions, with fractal interpolation outperforming linear interpolation. This study provides new solutions and methods for predicting small sample financial time series.