From GARCH to Neural Network for Volatility Forecast

ArXiv ID: 2402.06642 “View on arXiv”

Authors: Unknown

Abstract

Volatility, as a measure of uncertainty, plays a crucial role in numerous financial activities such as risk management. The Econometrics and Machine Learning communities have developed two distinct approaches for financial volatility forecasting: the stochastic approach and the neural network (NN) approach. Despite their individual strengths, these methodologies have conventionally evolved in separate research trajectories with little interaction between them. This study endeavors to bridge this gap by establishing an equivalence relationship between models of the GARCH family and their corresponding NN counterparts. With the equivalence relationship established, we introduce an innovative approach, named GARCH-NN, for constructing NN-based volatility models. It obtains the NN counterparts of GARCH models and integrates them as components into an established NN architecture, thereby seamlessly infusing volatility stylized facts (SFs) inherent in the GARCH models into the neural network. We develop the GARCH-LSTM model to showcase the power of the GARCH-NN approach. Experiment results validate that amalgamating the NN counterparts of the GARCH family models into established NN models leads to enhanced outcomes compared to employing the stochastic and NN models in isolation.

Keywords: volatility forecasting, GARCH, neural networks (NN), LSTM, financial econometrics, General Financial Instruments

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper introduces significant mathematical complexity by establishing equivalence relationships between GARCH models and neural network counterparts, requiring advanced econometric and machine learning theory. Empirical rigor is demonstrated through experiments on five globally traded equities datasets and Value at Risk (VaR) computation, showing backtest-ready implementation with specific performance comparisons.

  flowchart TD
    A["Research Goal: Bridge Gap<br>between GARCH and NN<br>for Volatility Forecasting"] --> B["Key Methodology: Establish<br>Equivalence Relationship<br>between GARCH & NN Models"]
    B --> C["Develop GARCH-NN Approach<br>Integrate GARCH NN-counterparts<br>into NN Architecture"]
    C --> D{"Computational Process"}
    D --> E["Data Input: Financial Time Series"]
    D --> F["Model 1: Stochastic Approach<br>e.g., Standard GARCH"]
    D --> G["Model 2: Pure NN Approach<br>e.g., LSTM"]
    D --> H["Model 3: Proposed Method<br>GARCH-LSTM"]
    E --> F & G & H
    F & G & H --> I["Key Outcomes: Enhanced<br>Forecasting Performance<br>via Hybrid Architecture"]