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This paper shows a novel machine learning model for realized volatility (RV)prediction using a normalizing flow, an invertible neural network. Since RV isknown to be skewed and have a fat tail, previous methods transform RV intovalues that follow a latent distribution with an explicit shape and then applya prediction model. However, knowing that shape is non-trivial, and thetransformation result influences the prediction model. This paper proposes tojointly train the transformation and the prediction model. The training processfollows a maximum-likelihood objective function that is derived from theassumption that the prediction residuals on the transformed RV time series arehomogeneously Gaussian. The objective function is further approximated using anexpectation-maximum algorithm. On a dataset of 100 stocks, our methodsignificantly outperforms other methods using analytical or naiveneural-network transformations.

Co-Training Realized Volatility Prediction Model with Neural Distributional Transformation