Hyperparameters for LSTM network.

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.