Volatility analysis via coupled Wishart process

The study of volatility has been a great concern to people both from academia and industry. Recently, several stochastic approaches such as the Wishart process, have been proposed to model the volatility with strong capturing power and flexibility. However, these kinds of models and their deviations only tackle several variables from only one system. But in real world, individuals and systems are more or less related to each other via explicit or implicit relationships. In this paper, we propose a coupled Wishart process model to capture such couplings when modeling the volatility, in which a linear approach is introduced. A learning algorithm is then adopted for this coupled model based on the Markov chain Monte Carlo (MCMC) methods, namely Gibbs sampling and Metropolis-Hasting sampling. Substantial experiments on both synthetic and real-life data demonstrate that the coupled Wishart process can effectively capture the coupling relationship across different systems and outperforms the single Wishart process in terms of modeling and analyzing volatility.