LSTM

Explainable Prediction of Economic Time Series Using IMFs and Neural Networks ArXiv ID: 2512.12499 “View on arXiv” Authors: Pablo Hidalgo, Julio E. Sandubete, Agustín García-García Abstract This study investigates the contribution of Intrinsic Mode Functions (IMFs) derived from economic time series to the predictive performance of neural network models, specifically Multilayer Perceptrons (MLP) and Long Short-Term Memory (LSTM) networks. To enhance interpretability, DeepSHAP is applied, which estimates the marginal contribution of each IMF while keeping the rest of the series intact. Results show that the last IMFs, representing long-term trends, are generally the most influential according to DeepSHAP, whereas high-frequency IMFs contribute less and may even introduce noise, as evidenced by improved metrics upon their removal. Differences between MLP and LSTM highlight the effect of model architecture on feature relevance distribution, with LSTM allocating importance more evenly across IMFs. ...

Stochastic Volatility Modelling with LSTM Networks: A Hybrid Approach for S&P 500 Index Volatility Forecasting ArXiv ID: 2512.12250 “View on arXiv” Authors: Anna Perekhodko, Robert Ślepaczuk Abstract Accurate volatility forecasting is essential in banking, investment, and risk management, because expectations about future market movements directly influence current decisions. This study proposes a hybrid modelling framework that integrates a Stochastic Volatility model with a Long Short Term Memory neural network. The SV model improves statistical precision and captures latent volatility dynamics, especially in response to unforeseen events, while the LSTM network enhances the model’s ability to detect complex nonlinear patterns in financial time series. The forecasting is conducted using daily data from the S and P 500 index, covering the period from January 1 1998 to December 31 2024. A rolling window approach is employed to train the model and generate one step ahead volatility forecasts. The performance of the hybrid SV-LSTM model is evaluated through both statistical testing and investment simulations. The results show that the hybrid approach outperforms both the standalone SV and LSTM models and contributes to the development of volatility modelling techniques, providing a foundation for improving risk assessment and strategic investment planning in the context of the S and P 500. ...

The Red Queen’s Trap: Limits of Deep Evolution in High-Frequency Trading ArXiv ID: 2512.15732 “View on arXiv” Authors: Yijia Chen Abstract The integration of Deep Reinforcement Learning (DRL) and Evolutionary Computation (EC) is frequently hypothesized to be the “Holy Grail” of algorithmic trading, promising systems that adapt autonomously to non-stationary market regimes. This paper presents a rigorous post-mortem analysis of “Galaxy Empire,” a hybrid framework coupling LSTM/Transformer-based perception with a genetic “Time-is-Life” survival mechanism. Deploying a population of 500 autonomous agents in a high-frequency cryptocurrency environment, we observed a catastrophic divergence between training metrics (Validation APY $>300%$) and live performance (Capital Decay $>70%$). We deconstruct this failure through a multi-disciplinary lens, identifying three critical failure modes: the overfitting of \textit{“Aleatoric Uncertainty”} in low-entropy time-series, the \textit{“Survivor Bias”} inherent in evolutionary selection under high variance, and the mathematical impossibility of overcoming microstructure friction without order-flow data. Our findings provide empirical evidence that increasing model complexity in the absence of information asymmetry exacerbates systemic fragility. ...

Integrating LSTM Networks with Neural Levy Processes for Financial Forecasting ArXiv ID: 2512.07860 “View on arXiv” Authors: Mohammed Alruqimi, Luca Di Persio Abstract This paper investigates an optimal integration of deep learning with financial models for robust asset price forecasting. Specifically, we developed a hybrid framework combining a Long Short-Term Memory (LSTM) network with the Merton-Lévy jump-diffusion model. To optimise this framework, we employed the Grey Wolf Optimizer (GWO) for the LSTM hyperparameter tuning, and we explored three calibration methods for the Merton-Levy model parameters: Artificial Neural Networks (ANNs), the Marine Predators Algorithm (MPA), and the PyTorch-based TorchSDE library. To evaluate the predictive performance of our hybrid model, we compared it against several benchmark models, including a standard LSTM and an LSTM combined with the Fractional Heston model. This evaluation used three real-world financial datasets: Brent oil prices, the STOXX 600 index, and the IT40 index. Performance was assessed using standard metrics, including Mean Squared Error (MSE), Mean Absolute Error(MAE), Mean Squared Percentage Error (MSPE), and the coefficient of determination (R2). Our experimental results demonstrate that the hybrid model, combining a GWO-optimized LSTM network with the Levy-Merton Jump-Diffusion model calibrated using an ANN, outperformed the base LSTM model and all other models developed in this study. ...

Technical Analysis Meets Machine Learning: Bitcoin Evidence ArXiv ID: 2511.00665 “View on arXiv” Authors: José Ángel Islas Anguiano, Andrés García-Medina Abstract In this note, we compare Bitcoin trading performance using two machine learning models-Light Gradient Boosting Machine (LightGBM) and Long Short-Term Memory (LSTM)-and two technical analysis-based strategies: Exponential Moving Average (EMA) crossover and a combination of Moving Average Convergence/Divergence with the Average Directional Index (MACD+ADX). The objective is to evaluate how trading signals can be used to maximize profits in the Bitcoin market. This comparison was motivated by the U.S. Securities and Exchange Commission’s (SEC) approval of the first spot Bitcoin exchange-traded funds (ETFs) on 2024-01-10. Our results show that the LSTM model achieved a cumulative return of approximately 65.23% in under a year, significantly outperforming LightGBM, the EMA and MACD+ADX strategies, as well as the baseline buy-and-hold. This study highlights the potential for deeper integration of machine learning and technical analysis in the rapidly evolving cryptocurrency landscape. ...

From Headlines to Holdings: Deep Learning for Smarter Portfolio Decisions ArXiv ID: 2509.24144 “View on arXiv” Authors: Yun Lin, Jiawei Lou, Jinghe Zhang Abstract Deep learning offers new tools for portfolio optimization. We present an end-to-end framework that directly learns portfolio weights by combining Long Short-Term Memory (LSTM) networks to model temporal patterns, Graph Attention Networks (GAT) to capture evolving inter-stock relationships, and sentiment analysis of financial news to reflect market psychology. Unlike prior approaches, our model unifies these elements in a single pipeline that produces daily allocations. It avoids the traditional two-step process of forecasting asset returns and then applying mean–variance optimization (MVO), a sequence that can introduce instability. We evaluate the framework on nine U.S. stocks spanning six sectors, chosen to balance sector diversity and news coverage. In this setting, the model delivers higher cumulative returns and Sharpe ratios than equal-weighted and CAPM-based MVO benchmarks. Although the stock universe is limited, the results underscore the value of integrating price, relational, and sentiment signals for portfolio management and suggest promising directions for scaling the approach to larger, more diverse asset sets. ...

Predictive Performance of LSTM Networks on Sectoral Stocks in an Emerging Market: A Case Study of the Pakistan Stock Exchange ArXiv ID: 2509.14401 “View on arXiv” Authors: Ahad Yaqoob, Syed M. Abdullah Abstract The application of deep learning models for stock price forecasting in emerging markets remains underexplored despite their potential to capture complex temporal dependencies. This study develops and evaluates a Long Short-Term Memory (LSTM) network model for predicting the closing prices of ten major stocks across diverse sectors of the Pakistan Stock Exchange (PSX). Utilizing historical OHLCV data and an extensive set of engineered technical indicators, we trained and validated the model on a multi-year dataset. Our results demonstrate strong predictive performance ($R^2 > 0.87$) for stocks in stable, high-liquidity sectors such as power generation, cement, and fertilizers. Conversely, stocks characterized by high volatility, low liquidity, or sensitivity to external shocks (e.g., global oil prices) presented significant forecasting challenges. The study provides a replicable framework for LSTM-based forecasting in data-scarce emerging markets and discusses implications for investors and future research. ...

Investment Portfolio Optimization Based on Modern Portfolio Theory and Deep Learning Models ArXiv ID: 2508.14999 “View on arXiv” Authors: Maciej Wysocki, Paweł Sakowski Abstract This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio optimization, which is based on deep learning models. We employ the long short-term memory (LSTM) recurrent neural networks (RNN) along with two probabilistic deep learning models: DeepVAR and GPVAR to the task of one-day ahead multivariate forecasting. We then use these forecasts to optimize portfolios of stocks and cryptocurrencies. Our analysis presents results across different combinations of observation windows and rebalancing periods to compare performances of classical and deep learning variance-covariance estimation methods. The conclusions of the study are that although the strategies (portfolios) performance differed significantly between different combinations of parameters, generally the best results in terms of the information ratio and annualized returns are obtained using the LSTM-RNN models. Moreover, longer observation windows translate into better performance of the deep learning models indicating that these methods require longer windows to be able to efficiently capture the long-term dependencies of the variance-covariance matrix structure. Strategies with less frequent rebalancing typically perform better than these with the shortest rebalancing windows across all considered methods. ...

Alternative Loss Function in Evaluation of Transformer Models ArXiv ID: 2507.16548 “View on arXiv” Authors: Jakub Michańków, Paweł Sakowski, Robert Ślepaczuk Abstract The proper design and architecture of testing machine learning models, especially in their application to quantitative finance problems, is crucial. The most important aspect of this process is selecting an adequate loss function for training, validation, estimation purposes, and hyperparameter tuning. Therefore, in this research, through empirical experiments on equity and cryptocurrency assets, we apply the Mean Absolute Directional Loss (MADL) function, which is more adequate for optimizing forecast-generating models used in algorithmic investment strategies. The MADL function results are compared between Transformer and LSTM models, and we show that in almost every case, Transformer results are significantly better than those obtained with LSTM. ...

Optimization Method of Multi-factor Investment Model Driven by Deep Learning for Risk Control ArXiv ID: 2507.00332 “View on arXiv” Authors: Ruisi Li, Xinhui Gu Abstract Propose a deep learning driven multi factor investment model optimization method for risk control. By constructing a deep learning model based on Long Short Term Memory (LSTM) and combining it with a multi factor investment model, we optimize factor selection and weight determination to enhance the model’s adaptability and robustness to market changes. Empirical analysis shows that the LSTM model is significantly superior to the benchmark model in risk control indicators such as maximum retracement, Sharp ratio and value at risk (VaR), and shows strong adaptability and robustness in different market environments. Furthermore, the model is applied to the actual portfolio to optimize the asset allocation, which significantly improves the performance of the portfolio, provides investors with more scientific and accurate investment decision-making basis, and effectively balances the benefits and risks. ...