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A new model for time-series forecasting using radial basis functions and exogenous data

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Abstract

In this paper, we present a new model for time-series forecasting using radial basis functions (RBFs) as a unit of artificial neural networks (ANNs), which allows the inclusion of exogenous information (EI) without additional pre-processing. We begin by summarizing the most well-known EI techniques used ad hoc, i.e., principal component analysis (PCA) and independent component analysis (ICA). We analyze the advantages and disadvantages of these techniques in time-series forecasting using Spanish bank and company stocks. Then, we describe a new hybrid model for time-series forecasting which combines ANNs with genetic algorithms (GAs). We also describe the possibilities when implementing the model on parallel processing systems.

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Notes

  1. Before discussing this problem, we prove the existence of an exact representation for the continuous function in terms of simpler functions using Kolmogorov’s theorem.

  2. The subindex k is related to the structure or subset of loss functions used in the approximation.

  3. Roughly speaking, the VC dimension, h, measures how many training points can be separated for all possible labeling using functions of the class.

  4. In the strict sense presented in [33], that is, they are bounded functions or satisfy a certain inequality.

  5. For example, Vapnik’s ε insensitive loss function [33]: \(L{\left( {f{\left( x \right)} - y} \right)} = \left\{ {\begin{array}{*{20}l} {{{\left| {f{\left( x \right)} - y} \right|} - \varepsilon } \hfill} & {{{\text{for }}{\left| {f{\left( x \right)} - y} \right|} \geqslant \varepsilon } \hfill} \\ {0 \hfill} & {{{\text{otherwise}}} \hfill} \\ \end{array} } \right. \)

  6. This calculation must be performed several times during the process.

  7. Generalized differentiation of a function: \({\text{d}}R{\left| f \right|} = {\left[ {{\left( {{\text{d}} \mathord{\left/ {\vphantom {{\text{d}} {{\text{d}}\rho }}} \right. \kern-\nulldelimiterspace} {{\text{d}}\rho }} \right)}R{\left[ {f + \rho h} \right]}} \right]}, \) where h∈H.

  8. The principal feature of these algorithms is the sequential adaptation of neural resources.

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Authors and Affiliations

  1. Department of Systems Engineering and Automation, Electronic Technology and Electronics, University of Cádiz, Spain

    J. M. Górriz & J. J. G. de la Rosa

  2. Department of Computer Architecture and Computer Technology, University of Granada, Spain

    C. G. Puntonet & M. Salmerón

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  1. J. M. Górriz
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  2. C. G. Puntonet
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  3. M. Salmerón
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  4. J. J. G. de la Rosa
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Correspondence to J. M. Górriz.

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Górriz, J.M., Puntonet, C.G., Salmerón, M. et al. A new model for time-series forecasting using radial basis functions and exogenous data. Neural Comput & Applic 13, 101–111 (2004). https://doi.org/10.1007/s00521-004-0412-5

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