Co-Training Realized Volatility Prediction Model with Neural Distributional Transformation
Co-Training Realized Volatility Prediction Model with Neural Distributional Transformation
This paper introduces a co-training framework for realized volatility (RV) prediction that jointly optimizes a neural distributional transformation and a prediction model. The transformation is implemented via a normalizing flow using neural ordinary differential equations (NODE), which provides an invertible mapping from raw RV to a latent Gaussian-like distribution. The prediction model is a heterogeneous autoregressive (HAR) model applied to the transformed series. The joint training is formulated as a maximum-likelihood problem and solved via an expectation-maximization (EM) algorithm, where the prediction residuals are assumed to be homogeneous Gaussian. Experiments on 100 NYSE stocks over 480 trading days show that the proposed method significantly outperforms baselines using identity, analytical (Wallace, Yeo-Johnson), or simple neural network (tanh) transformations, both in terms of log-likelihood and RMSE. The results demonstrate that co-training the transformation with the prediction model effectively captures the skewed and fat-tailed distribution of RV while maintaining predictive accuracy.
Highlights
- 1Proposes a novel co-training framework that jointly optimizes a normalizing flow transformation and a HAR prediction model for realized volatility.
- 2Uses neural ordinary differential equations (NODE) as an invertible transformation to handle the skewed and fat-tailed distribution of RV.
- 3Derives a maximum-likelihood objective with an expectation-maximization algorithm for joint training.
- 4Outperforms analytical transformations (Box-Cox, Yeo-Johnson) and simple neural network transformations on 100 NYSE stocks.
Methods
- MNormalizing flow via neural ordinary differential equations (NODE) for invertible distributional transformation.
- MHeterogeneous autoregressive (HAR) model for time-series prediction of transformed RV.
- MExpectation-maximization (EM) algorithm for co-training transformation and prediction parameters.
- MResidual density estimation assuming homogeneous Gaussian distribution for prediction errors.
Results
- RThe proposed co-trained NODE+HAR model significantly outperforms identity, Wallace, Yeo-Johnson, and tanh transformations in terms of log-likelihood and RMSE.
- RUsing a Gaussian residual assumption is sufficient after normalizing flow transformation, unlike raw RV where residuals are skewed.
- RThe method effectively captures the long-memory and fat-tail characteristics of realized volatility.
- RJoint training yields better predictive performance than separate estimation of transformation and prediction.
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