Adaptive kernel algorithms for time series prediction

Marcin Michalak

Abstract


The article describes two kernel algorithms of the regression function estimation, that are used for the time series prediction. First of them (HASKE) has its own heuristic of the h parameter evaluation. The second (HKSVR) connects SVM and the HASKE in such way that it is based on the HASKE heuristic of local neighborhood evaluation.

Keywords


time series prediction; kernel estimators; nonparametric regression; support vectors machines

Full Text:

PDF

References


S&P500 historical data. http://stooq.pl/q/d/?s=s%26p500.

de Boor C: A practical guide to splines. Springer, 2001.

Boser B. E., Guyon I. M., Vapnik V. N.: A training algorithm for optimal margin classifiers. In Proc. of the 5th annual workshop on Computational learning theory, Pittsburgh 1992, s. 144-152.

Box G. E. P., Jenkins G. M.: Analiza szeregów czasowych. PWN, Warszawa 1983.

Cao L. J., Tay F. E. H.: Svm with adaptive parameters in financial time series forecasting. IEEE Trans, on Neural Networks, 14(6), 2003, s. 1506-1518.

Cleveland W. S., Devlin S. J.: Locally weighted regression. Jour, of the Am. Stat. Ass.,83(403), 1988, s. 596-610.

Epanechnikov V. A.: Nonparametric estimation of a multivariate probability density. Theory of Probability and Its Applications, 14,1969, s. 153-158.

Fan J., Gijbels I.: Variable bandwidth and local linear regression smoothers. Annals of Statistics, 20(4), 1992, s. 2008-2036.

Fernandez R.: Predicting time series with a local support vector regression machine. In Proc. of the ECCAI Advanced Course on Artificial Intelligence '99.

Friedman J. H.: Multivariate adaptive regression splines. Annals of Statistics, 19(1), 1991,s. 1-141.

Gajek L., Kałuszka M.: Wnioskowanie statystyczne. WNT, Warszawa 2000.

Gasser T., Kneip A., Kohler W.: A flexible and fast method for automatic smoothing. Jour, of the Am. Stat. Ass., 86(415), 1991, s. 643-652.

Gasser T., Muller H. G.: Estimating regression function and their derivatives by the kernel method. Scandinavian Journal of Statistics, 11,1984, s. 171-185.

Hastie T. J., Tibshirani R. J.: Generalized Additive Models. Chapman & Hall/CRC, 1990.

Huang K., Yang H., King I., Lyu M.: Local svr for financial time series prediction. In Proc of IJCNN'06, Vancouver 2006, s. 1622-1627.

Kaastra I., Boyd M.: Designing a neural network for forecasting financial and economic time series. Neurocomputing, 10(3), 1996, s. 215-236.

Koronacki J., Ćwik J.: Statystyczne systemy uczące się. WNT, Warszawa 2005.

Kulczycki P.: Estymatory jądrowe w analizie systemowej. WNT, Warszawa 2005.

Michalak M.: Możliwości poprawy jakości usług w transporcie miejskim poprzez monitoring natężenia potoków pasażerskich. In ITS dla Śląska, Katowice 2008.

Michalak M., Stąpor K.: Estymacja jądrowa w predykcji szeregów czasowych. Studia Informatica, Vol. 29, No 3A(78), Gliwice 2008, s. 71 -90.1-141.

Muller K. R., Smolą A. J., Ratsch G., Scholkopf B., Kohlmorgen J., Vapnik V.: Predicting time series with support vector machines. In Proceedings of the 7th ICANN, LNCS(1327), Springer-Verlag, London 1997, s. 999-1004.

Nadaraya E. A.: On estimating regression. Theory of Probability and Its Applications, 9(1), 1964, s. 141-142.

Scholkopf B., Smola A.: Learning with Kernels. MIT Press, 2002.

Sikora M., Kozielski M., Michalak M.: Innowacyjne narzędzia informatyczne analizy danych. Wydział Transportu, Gliwice 2008.

Silverman B. W.: Density Estimation for Statistics and Data Analysis. Chapman & Hall, 1986.

Smola A. J.: Regression estimation with support vector learning machines. Master's thesis, Technische Universitat Munchen 1996.

Smola A. J., Scholkopf B.: A tutorial on support vector regression. Statistics and Computing, 14(3), 2004, s. 199-222.

Taylor J. S., Cristianini N.: Kernel Methods for Pattern Analysis. Cambridge University Press, 2004.

Terrell G. R... The maximal smoothing principle in density estimation. Jour, of the Am. Stat. Ass., 85(410), 1990, s. 470-477.

Terrell G. R., Scott D. W.: Variable kernel density estimation. Annals of Statistics, 20(3), 1992, s. 1236-1265.

Turlach B. A.: Bandwidth selection in kernel density estimation: A review. Technical report, Universite Catholique de Louvain, 1993.

Vapnik V. N.: Statistical Learning Theory. Wiley, 1988.

Wand M. P., Jones M. C: Kernel Smoothing. Chapman & Hall, 1995.

Watson G. S.: Smooth regression analysis. Sankhya - The Indian Journal of Statistics, 26(4), 1964, s. 359-372.




DOI: http://dx.doi.org/10.21936/si2009_v30.n3A.437