Volatility-informed SPY forecasting: From CGR-SPY analysis to DLSTM prediction

Hong Cao, Hao Chen, Yulong Lian and Hong-Kun Zhang

PLOS Complex Systems, 2025, vol. 2, issue 8, 1-16

Abstract: Forecasting stock returns is a vital and at the same time challenging task in the financial arena, given the market’s susceptibility to abrupt swings. In this paper, we propose a strategy that adapts to different volatility regimes: during periods of high volatility, we employ the copper-gold ratio (CGR) as a leading indicator for the S&P 500 (SPY), while in periods of normal volatility, we introduce a differential long-term memory (DLSTM) neural network. The CGR combines the properties of copper (which reflects industrial and economic activity) and gold, a traditional safe-haven asset. In four major economic events, our analysis reveals that sharp movements in the CGR often precede corresponding changes in the SPY, suggesting the ratio’s potential as an early warning signal. For more stable markets, we introduce the DLSTM, which extends the standard LSTM architecture through a loss function designed to exploit differences between consecutive price steps. This design increases predictive power and achieves 82% directional accuracy on daily SPY forecasts, outperforming both a baseline LSTM and a binary classification approach. Finally, we validate the trading utility of the DLSTM by simulating intraday trading over one- and three-month periods, demonstrating consistent gains that highlight the practical value of the method. By synthesizing CGR analysis and DLSTM modeling, our approach offers a versatile framework to address diverse market environments and provide new insights for both researchers and practitioners.Author summary: Predicting stock movements can be challenging, especially when markets change rapidly. This study addresses the challenge by proposing a two-part approach to forecasting the S&P 500 (SPY) under different market conditions. During periods of high volatility, we use the copper-to-gold ratio (CGR). Copper’s value often tracks economic activity, while gold remains stable during financial turmoil, making their ratio a potential early warning indicator of stock price movements. Then, during quieter times, we introduce a specialized neural network called the difference long-short-term memory (DLSTM). The LSTM is a machine learning tool designed to remember important information over time, which is critical for financial data. Our DLSTM extends the LSTM by focusing on price changes between consecutive days, resulting in stronger predictive power. Tests show that it achieves 82% accuracy in predicting daily price trends, outperforming simpler models. We also validate these predictions using a simulated trading strategy that shows consistent gains over a one- and three-month period. By combining CGR and DLSTM, this study provides an adaptable approach for investors navigating today’s unpredictable markets.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcsy00:0000037

DOI: 10.1371/journal.pcsy.0000037

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