Co-Training Realized Volatility Prediction Model with Neural Distributional Transformation

ArXiv ID: 2310.14536 “View on arXiv”

Authors: Unknown

Abstract

This paper shows a novel machine learning model for realized volatility (RV) prediction using a normalizing flow, an invertible neural network. Since RV is known to be skewed and have a fat tail, previous methods transform RV into values that follow a latent distribution with an explicit shape and then apply a prediction model. However, knowing that shape is non-trivial, and the transformation result influences the prediction model. This paper proposes to jointly train the transformation and the prediction model. The training process follows a maximum-likelihood objective function that is derived from the assumption that the prediction residuals on the transformed RV time series are homogeneously Gaussian. The objective function is further approximated using an expectation-maximum algorithm. On a dataset of 100 stocks, our method significantly outperforms other methods using analytical or naive neural-network transformations.

Keywords: Realized Volatility, Normalizing Flow, Invertible Neural Networks, Maximum Likelihood, Expectation-Maximization, Equity

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts such as normalizing flows, maximum-likelihood estimation with EM approximation, and distribution theory, indicating high mathematical complexity. It also demonstrates empirical rigor by testing on a substantial dataset (100 stocks), comparing against multiple baselines, and detailing the implementation and training process for the neural network and prediction model.

  flowchart TD
    A["Research Goal: Realized Volatility Prediction<br/>with Skewed/Fat-Tail Data"] --> B["Data: 100 Stocks"]
    B --> C["Method: Co-Training Flow & Model"]
    C --> D["Normalization: Invertible Neural Network<br/>Transforms RV to Latent Gaussian"]
    D --> E["Forecasting: Neural Network<br/>Predicts Transformed RV"]
    E --> F["Training: Max Likelihood via EM Algorithm"]
    F --> G["Outcome: Jointly Optimized Model"]
    G --> H["Result: Significantly Outperforms<br/>Analytical/Naive Transformations"]