Abstract
A hierarchical mixture of autoregressive (AR) models is proposed for the analysis of nonlinear time-series. The model is a decision tree with soft sigmoidal splits at the inner nodes and linear autoregressive models at the leaves. The global prediction of the mixture is a weighted average of the partial predictions from each of the AR models. The weights in this average are computed by the application of the hierarchy of soft splits at the inner nodes of the tree on the input, which consists in the vector of the delayed values of the time series. The weights can be interpreted as a priori probabilities that an example is generated by the AR model at that leaf. As an illustration of the flexibility and robustness of the models generated by these mixtures, an application to the analysis of a financial time-series is presented.
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References
M. I. Jordan and R. A. Jacobs. Hierarchical mixtures of experts and the EM algorithm. Neural Computation, 6:181–214, 1994.
A. Suárez and J. F. Lutsko. Globally optimal fuzzy decision trees for classification and regression. IEEE Trans. on Pattern Analysis and Machine Intelligence, 21(12):1297–1311, 1999.
V. Medina-Chico, A. Suárez, and J. F. Lutsko. Backpropagation in decision trees for regression. In Luc De Raedt and Peter Flach, editors, Lecture Notes in Artificial Intelligence: Proceedings of the 12th European Conference on Machine Learning, volume 2167, pages 348–359, Berlin, 2001. Springer.
M. I. Jordan and R. A. Jacobs. Adaptive mixtures of local experts. Neural Computation, 3:79–87, 1991.
R. Jacobs and M. Tanner. Mixtures of X. In A. J. C. Sharkey, editor, Combining Artificial Neural Nets, pages 267–296, London, 1999. Springer.
C. Schittenkopf and G. Dorffner. Risk-neutral density extraction from option prices: Improved pricing with mixture density networks. IEEE Transactions on Neural Networks, 12(4):716–725, 2001.
A. S. Weigend, M. Mangeas, and A. N. Srivastava. Nonlinear gated experts for time series: Discovering regimes and avoiding overfitting. International Journal of Neural Systems, 6(4):373–399, 1995.
C. S. Wong and W. K. Li. On a mixture autoregressive model. Journal of the Royal Statistical Society B, 62:95–115, 2000.
A. Suárez. Mixtures of autorregressive models for financial risk analysis. In J. R. Dorronsoro, editor, Lecture Notes in Computer Science: Artificial Neural Networks-ICANN 2002, volume 2167, pages 1186–1191, Berlin, 2002. Springer.
P. Jorion. Value at Risk: The new Benchmark for Controlling Market Risk. McGraw-Hill, New York, 1997.
E. Eberlein and U. Keller. Hyperbolic distributions in finance. Bernoulli, 1:281–299, 1995.
J. Hull and A. White. Value at risk when daily changes in market variables are not normally distributed. Journal of Derivatives, 5(3):9–19, 1998.
P. Embrechts, C. Kluplelberg, and T. Mikosch. Modelling Extremal Events for Insurance and Finance. Springer-Verlag, Berlin, 1997.
H. Tong. Non-linear Time Series. A Dynamical System Approach. Oxford University Press, New York, 1996.
G. González-Rivera. Smooth transition GARCH models. Studies in Nonlinear Dynamics and Econometrics, 3:61–78, 1998.
M. Rosenblatt. Remarks on a multivariate transformation. Annals of Mathematica Statistics, 23(3):470–472, 1952.
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Vidal, C., Suárez, A. (2003). Hierarchical Mixtures of Autoregressive Models for Time-Series Modeling. In: Kaynak, O., Alpaydin, E., Oja, E., Xu, L. (eds) Artificial Neural Networks and Neural Information Processing — ICANN/ICONIP 2003. ICANN ICONIP 2003 2003. Lecture Notes in Computer Science, vol 2714. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44989-2_71
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DOI: https://doi.org/10.1007/3-540-44989-2_71
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