Hybrid Models for Financial Forecasting: Combining Econometric, Machine Learning, and Deep Learning Models

ArXiv ID: 2505.19617 “View on arXiv”

Authors: Dominik Stempień, Robert Ślepaczuk

Abstract

This research systematically develops and evaluates various hybrid modeling approaches by combining traditional econometric models (ARIMA and ARFIMA models) with machine learning and deep learning techniques (SVM, XGBoost, and LSTM models) to forecast financial time series. The empirical analysis is based on two distinct financial assets: the S&P 500 index and Bitcoin. By incorporating over two decades of daily data for the S&P 500 and almost ten years of Bitcoin data, the study provides a comprehensive evaluation of forecasting methodologies across different market conditions and periods of financial distress. Models’ training and hyperparameter tuning procedure is performed using a novel three-fold dynamic cross-validation method. The applicability of applied models is evaluated using both forecast error metrics and trading performance indicators. The obtained findings indicate that the proper construction process of hybrid models plays a crucial role in developing profitable trading strategies, outperforming their individual components and the benchmark Buy&Hold strategy. The most effective hybrid model architecture was achieved by combining the econometric ARIMA model with either SVM or LSTM, under the assumption of a non-additive relationship between the linear and nonlinear components.

Keywords: Hybrid Modeling, ARIMA, LSTM, XGBoost, Cross-Validation, Equities / Cryptocurrency

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 9.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical concepts like fractional integration (ARFIMA) and combines them with deep learning (LSTM) and hybridization techniques, indicating high mathematical complexity. It demonstrates high empirical rigor by using over two decades of daily data for S&P 500 and nearly ten years for Bitcoin, implementing a novel three-fold dynamic cross-validation, and evaluating both forecast accuracy and real-world trading performance with multiple risk-adjusted metrics.

  flowchart TD
    A["Research Goal: Develop & Evaluate Hybrid Models for Financial Forecasting"]
    B["Data: S&P 500 (20+ yrs) & Bitcoin (10+ yrs)"]
    C["Methodology: 3-Fold Dynamic Cross-Validation & Hyperparameter Tuning"]
    D["Models: Econometric + ML/DL<br/>(ARIMA/ARFIMA + SVM/XGBoost/LSTM)"]
    E["Non-Additive Hybrid Construction"]
    F["Evaluation: Forecast Errors & Trading Metrics"]
    G["Key Findings: Hybrid Models Outperform Benchmarks<br/>Best: ARIMA + (SVM or LSTM)"]

    A --> B
    B --> C
    C --> D
    D --> E
    E --> F
    F --> G