A Bayesian nonlinear support vector machine error correction model

Van Gestel, T., Espinoza, M., Baesens, B., Suykens, J.A.K., Brasseur, C. and De Moor, B. (2006) A Bayesian nonlinear support vector machine error correction model. International Journal of Forecasting, 25 (2), 77-100. (doi:10.1002/for.975).

Abstract

The use of linear error correction models based on stationarity and cointegration analysis, typically estimated with least squares regression, is a common technique for financial time series prediction. In this paper, the same formulation is extended to a nonlinear error correction model using the idea of a kernel-based implicit nonlinear mapping to a high-dimensional feature space in which linear model formulations are specified. Practical expressions for the nonlinear regression are obtained in terms of the positive definite kernel function by solving a linear system. The nonlinear least squares support vector machine model is designed within the Bayesian evidence framework that allows us to find appropriate trade-offs between model complexity and in-sample model accuracy. From straightforward primal-dual reasoning, the Bayesian framework allows us to derive error bars on the prediction in a similar way as for linear models and to perform hyperparameter and input selection. Starting from the results of the linear modelling analysis, the Bayesian kernel-based prediction is successfully applied to out-of-sample prediction of an aggregated equity price index for the European chemical sector.

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Contributors

Author: B. Baesens

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