Volatility Prediction by Treed Gaussian Process With Limiting Linear Model

Abstract

In this paper, we present new hybrid models of financial volatility using treed Gaussian processes with jumps to the limiting linear model (TGPLLM) based on GARCH, EGARCH, and GJR models. The TGPLLM is modelled as three different volatility forms denoted as TGPLLM-GARCH, TGPLLM-EGARCH, and TGPLLM-GJR. Each of these models is trained by Matern family of correlation function as the correlation function is the heart of the Gaussian process. Hang Seng Index of Hong Kong stock market is analysed to check the predictive accuracy of the proposed models. The empirical results show that the hybrid models contribute improved predictive capability rather than the stationary GARCH, EGARCH, and GJR models for all cases. It is found that the hybrid Gaussian processes can significantly capture leverage effect of news.