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A Bayesian nonlinear support vector machine error correction model
Author(s) -
Van Gestel Tony,
Espinoza Marcelo,
Baesens Bart,
Suykens Johan A. K.,
Brasseur Carine,
De Moor Bart
Publication year - 2006
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.975
Subject(s) - hyperparameter , computer science , linear model , model selection , bayesian probability , support vector machine , least squares support vector machine , kernel (algebra) , nonlinear system , bayesian linear regression , hyperparameter optimization , cointegration , algorithm , bayesian inference , kernel method , mathematical optimization , mathematics , artificial intelligence , machine learning , physics , combinatorics , quantum mechanics
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. Copyright © 2006 John Wiley & Sons, Ltd.