Comparative analysis of financial data differentiation techniques using LSTM neural network

ArXiv ID: 2505.19243 “View on arXiv”

Authors: Dominik Stempień, Janusz Gajda

Abstract

We compare traditional approach of computing logarithmic returns with the fractional differencing method and its tempered extension as methods of data preparation before their usage in advanced machine learning models. Differencing parameters are estimated using multiple techniques. The empirical investigation is conducted on data from four major stock indices covering the most recent 10-year period. The set of explanatory variables is additionally extended with technical indicators. The effectiveness of the differencing methods is evaluated using both forecast error metrics and risk-adjusted return trading performance metrics. The findings suggest that fractional differentiation methods provide a suitable data transformation technique, improving the predictive model forecasting performance. Furthermore, the generated predictions appeared to be effective in constructing profitable trading strategies for both individual assets and a portfolio of stock indices. These results underline the importance of appropriate data transformation techniques in financial time series forecasting, supporting the application of memory-preserving techniques.

Keywords: Fractional Differencing, Time Series Forecasting, Machine Learning, Data Transformation, Stock Indices, Equities

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like fractional differencing operators (Granger-Joyeux/Hosking) and ARFIMA/ARTFIMA model estimations, indicating high mathematical complexity. It also demonstrates strong empirical rigor through a rigorous backtesting framework covering 10 years of data, multiple assets, hyperparameter tuning, and evaluation via both forecast error and risk-adjusted trading metrics.

  flowchart TD
    Start(["Research Goal:<br>Compare Financial Data<br>Differentiation Techniques"]) --> Inputs
    Inputs["[Data Inputs:<br>4 Major Stock Indices<br>10-Year Period<br>+ Technical Indicators"]]
    
    Inputs --> Methods
    subgraph Methods ["Methodology: Data Preparation"]
        LR["Traditional Approach:<br>Logarithmic Returns"]
        FD["Fractional Differencing<br>with Parameter Estimation"]
        TE["Tempered Extension<br>of Fractional Differencing"]
    end
    
    Methods --> Processing
    subgraph Processing ["Computational Process"]
        ML["Advanced Machine Learning<br>(LSTM Neural Network)"]
    end
    
    Processing --> Evaluation
    subgraph Evaluation ["Evaluation Metrics"]
        FM["Forecast Error Metrics"]
        TR["Risk-Adjusted Return<br>Trading Performance Metrics"]
    end
    
    Evaluation --> Findings(["Key Findings/Outcomes:<br>Fractional methods improve predictive<br>performance & generate profitable<br>trading strategies across assets"])
    
    style Start fill:#e1f5fe
    style Findings fill:#f3e5f5