Automated Inference and Learning in Modelling Financial Volatility

This paper uses the Specific-to-General methodological approach that is widely used in science, in which problems with existing theories are resolved as the need arises, to illustrate a number of important developments in the modelling of univariate and multivariate financial volatility. Some of the difficulties in analysing time-varying univariate and multivariate conditional volatility and stochastic volatility include the number of parameters to be estimated, and the computational complexities associated with multivariate conditional volatility models and both univariate and multivariate stochastic volatility models. For these reasons, among others, automated inference in its present state requires modifications and extensions for modelling in empirical financial econometrics. As a contribution to the development of automated inference in modelling volatility, twenty important issues in the specification, estimation and testing of conditional and stochastic volatility models are discussed. A “Potential for Automation Rating” (PAR) index and recommendations regarding the possibilities for automated inference in modelling financial volatility are given in each case. *The author wishes to acknowledge helpful discussions with Manabu Asai, Massimiliano Caporin, Felix Chan, Rob Engle, Jiti Gao, Suhejla Hoti, Thierry Jeantheau, Shiqing Ling, Adrian Pagan, Peter Phillips, Peter Robinson, Ruey Tsay, Neil Shephard and Jun Yu, and the constructive comments and suggestions of the Editor and two referees. Some of the ideas in the paper were presented at the International Conference on Threshold Models and New Developments in Time Series, Hong Kong, July 2004, and in seminars at the Bank of Italy, Carlos III University of Madrid, Chinese University of Hong Kong, Complutense University, Curtin University of Technology, Ente Einaudi Rome, Fondazione Eni Enrico Mattei Milan, Hong Kong University of Science and Technology, National University of Singapore, University of Adelaide, University of Auckland, University of Canterbury, University of Las Palmas de Gran Canaria, University of Melbourne, University of Milan-Bicocca, University Pompeu Fabra, University of Venice “Ca’ Foscari”, and University of Vigo. The financial support of the Australian Research Council is greatly appreciated.