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Accurate prediction of volatility is one of the most important tasks in financial decision making. Recently, the hybrid models integrating artificial neural networks with GARCH-type models have been developed, and performance gains from the models have been found to be outstanding. However, there have been few studies of hybrid models considering the nature of the distribution of financial data. Distribution of volatility time-series is highly concentrated near zero, and such aspect can cause low prediction performance on the whole domain of probability density function because weights in the networks can be trained to obtain accurate prediction only for the high frequency region, that is, near zero. To overcome the challenge, we propose a new hybrid model with GARCH-type models based on a novel non-linear filtering method to mitigate concentration property of volatility. For the filtering, we utilize root-type functions that transform extremely left-biased and pointed distribution of original volatility to a volume-upped (VU) distribution shifted to the right. Long short-term memory (LSTM) is employed as the basic implementation model, and the realized volatility of S&#x0026;P 500 is predicted using the proposed models. It is found that the proposed hybrid model (VU-GARCH-LSTM) obtains 21.03&#x0025; performance gain with respect to the root mean square error (RMSE) against the mean performances of the existing hybrid models integrating LSTM with GARCH-type models. Furthermore, the proposed model improves prediction performance in the right domain region of label probability density by making the prediction distribution comparable to the label distribution.

A Hybrid Prediction Model Integrating GARCH Models With a Distribution Manipulation Strategy Based on LSTM Networks for Stock Market Volatility