NON-PARAMETRIC SEGMENTATION OF REGIME-SWITCHING TIME SERIES WITH OBLIQUE SWITCHING TREES
Alexei Bocharov, Bo Thiesson
2012
Abstract
We introduce a non-parametric approach for the segmentation in regime-switching time-series models. The approach is based on spectral clustering of target-regressor tuples and derives a switching regression tree, where regime switches are modeled by oblique splits. Our segmentation method is very parsimonious in the number of splits evaluated during the construction process of the tree–for a candidate node, the method only proposes one oblique split on regressors and a few targeted splits on time. The regime-switching model can therefore be learned efficiently from data. We use the class of ART time series models to serve as illustration, but because of the non-parametric nature of our segmentation approach, it readily generalizes to a wide range of time-series models that go beyond the Gaussian error assumption in ART models. Experimental results on S&P 1500 financial trading data demonstrates dramatically improved predictive accuracy for the exemplifying ART models.
References
- Bishop, C. M. (1995). Neural Networks for Pattern Recognition. Oxford University Press, Oxford.
- Breiman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J. (1984). Classification and Regression Trees. Wadsworth International Group, Belmont, California.
- Brodley, C. E. and Utgoff, P. E. (1995). Multivariate decision trees. Machine Learning, 19(1):45-77.
- Chaudhuri, P., Huang, M. C., Loh, W.-Y., and Yao, R. (1994). Piecewise polynomial regression trees. Statistica Sinica, 4:143-167.
- Chickering, D., Meek, C., and Rounthwaite, R. (2001). Efficient determination of dynamic split points in a decision tree. In Proc. of the 2001 IEEE International Conference on Data Mining, pages 91-98. IEEE Computer Society.
- DeGroot, M. (1970). Optimal Statistical Decisions. McGraw-Hill, New York.
- Dobra, A. and Gehrke, J. (2002). Secret: A scalable linear regression tree algorithm. In Proc. of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 481-487. ACM Press.
- Donath, W. E. and Hoffman, A. J. (1973). Lower bounds for the partitioning of graphs. IBM Journal of Research and Development, 17:420-425.
- Fiedler, M. (1973). Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 23:298-305.
- Gama, J. (1997). Oblique linear tree. In Proc. of the Second International Symposium on Intelligent Data Analysis, pages 187-198.
- Hamilton, J. (1994). Time Series Analysis. Princeton University Press, Princeton, New Jersey.
- Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57(2):357-84.
- Hamilton, J. D. (1990). Analysis of time series subject to changes in regime. Journal of Econometrics, 45:39- 70.
- Iyengar, V. S. (1999). Hot: Heuristics for oblique trees. In Proc. of the 11th IEEE International Conference on Tools with Artificial Intelligence, pages 91-98, Washington, DC. IEEE Computer Society.
- Jordan, M. I. and Jacobs, R. A. (1994). Hierarchical mixtures of experts and the EM algorithm. Neural Computation, 6:181-214.
- Li, K. C., Lue, H. H., and Chen, C. H. (2000). Interactive tree-structured regression via principal Hessian directions. Journal of the American Statistical Association, 95:547-560.
- Mandelbrot, B. (1966). Forecasts of future prices, unbiased markets, and martingale models. Journal of Business, 39:242-255.
- Mandelbrot, B. B. and Hudson, R. L. (2006). The (mis)Behavior of Markets: A Fractal View of Risk, Ruin And Reward. Perseus Books Group, New York.
- Meek, C., Chickering, D. M., and Heckerman, D. (2002). Autoregressive tree models for time-series analysis. In Proc. of the Second International SIAM Conference on Data Mining, pages 229-244. SIAM.
- Meila?, M. and Shi, J. (2001). Learning segmentation by random walks. In Advances in Neural Information Processing Systems 13, pages 873-879. MIT Press.
- Murthy, S. K., Kasif, S., and Salzberg, S. (1994). A system for induction of oblique decision trees. Journal of Artificial Intelligence Research, 2:1-32.
- Ng, A. Y., Jordan, M. I., and Weiss, Y. (2002). On spectral clustering: Analysis and an algorithm. In Advances in Neural Information Processing Systems 14, pages 849-856. MIT Press.
- Samuelson, P. (1965). Proof that properly anticipated prices fluctuate randomly. In Industrial Management Review, volume 6, pages 41-49.
- Shi, J. and Malik, J. (2000). Normalized Cuts and Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8):888-905.
- Tong, H. (1983). Threshold models in non-linear time series analysis. In Lecture notes in statistics, No. 21. Springer-Verlag.
- Tong, H. and Lim, K. S. (1980). Threshold autoregression, limit cycles and cyclical data- with discussion. Journal of the Royal Statistical Society, Series B, 42(3):245-292.
- von Luxburg, U. (2007). A tutorial on spectral clustering. Statistics and Computing, 17(4):395-416.
- Waterhouse, S. and Robinson, A. (1995). Non-linear prediction of acoustic vectors using hierarchical mixtures of experts. In Advances in Neural Information Processing Systems 7, pages 835-842. MIT Press.
- Weigend, A. S., Mangeas, M., and Srivastava, A. N. (1995). Nonlinear gated experts for time series: Discovering regimes and avoiding overfitting. International Journal of Neural Systems, 6(4):373-399.
- White, S. and Smyth, P. (2005). A spectral clustering approach to finding communities in graphs. In Proc. of the 5th SIAM International Conference on Data Mining. SIAM.
Paper Citation
in Harvard Style
Bocharov A. and Thiesson B. (2012). NON-PARAMETRIC SEGMENTATION OF REGIME-SWITCHING TIME SERIES WITH OBLIQUE SWITCHING TREES . In Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM, ISBN 978-989-8425-99-7, pages 116-125. DOI: 10.5220/0003758601160125
in Bibtex Style
@conference{icpram12,
author={Alexei Bocharov and Bo Thiesson},
title={NON-PARAMETRIC SEGMENTATION OF REGIME-SWITCHING TIME SERIES WITH OBLIQUE SWITCHING TREES},
booktitle={Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,},
year={2012},
pages={116-125},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003758601160125},
isbn={978-989-8425-99-7},
}
in EndNote Style
TY - CONF
JO - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods - Volume 2: ICPRAM,
TI - NON-PARAMETRIC SEGMENTATION OF REGIME-SWITCHING TIME SERIES WITH OBLIQUE SWITCHING TREES
SN - 978-989-8425-99-7
AU - Bocharov A.
AU - Thiesson B.
PY - 2012
SP - 116
EP - 125
DO - 10.5220/0003758601160125