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Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29210

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GMDH Modeling Based on Polynomial Spline Estimation and Its Applications
GMDH algorithm can well describe the internal structure of objects. In the process of modeling, automatic screening of model structure and variables ensure the convergence rate.This paper studied a new GMDH model based on polynomial spline  stimation. The polynomial spline function was used to instead of the transfer function of GMDH to characterize the relationship between the input variables and output variables. It has proved that the algorithm has the optimal convergence rate under some conditions. The empirical results show that the algorithm can well forecast Consumer Price Index (CPI).
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[1] Ivakhnenko A. G. Heuristic self-organization on problems of engineering cybernetics. Automatic. 1970, 6(3), pp. 207-219.
[2] Liu G Z,Yan K Q,Kang Y L. GMDH- type Neural Network Algorithm and its Application. Mathematics in Practice and Theory. 2001, 31(4), pp. 464-469.
[3] He C Z, Lv J P. Study of Self-organizing Data Mining Theory and the Complexity of Economic Systems. Systems Engineering -Theory & Practice. 2001, 12, pp. 1-5.
[4] Johann Adolf Muller, Frank Lemke. Self-Organizing Data Mining. Libri Books. Dresden, Berlin.2000, pp. 67-110.
[5] Godfrey C. Onwubolu. Design of hybrid differential evolution and group method of data handling networks for modeling and prediction. Information Sci. 2008,178, pp. 3616– 3634.
[6] Petr Buryana and Godfrey C. Onwubolub. Design of enhanced MIA-GMDH learning networks. International Journal of Systems Science. 2001, 42(4), pp. 673-693.
[7] Tian Y X, Tan D J. GMDH Modeling for Forecasting Based on Local Linear Kernel Estimation. Journal of Systems Engineering. 2008, 23(1), pp. 9-15.
[8] Meysam Shaverdi, Saeed Fallahi, Vahhab Bashiri. Prediction of Stock Price of Iranian Petrochemical Industry Using GMDH-Type Neural Network and Genetic algorithm. Applied Mathematical Sciences, 2012, 6(7), pp. 319 – 332.
[9] Ye A Z. Nonparametric Econometrics. Nankai University Press. Tianjin. 2003, pp. 82-92.
[10] Jianhua Z.Huang and Haipeng Shen. Functional Coefficient Regression Models for Non-linear Time Series: A Polynomial Spline Approach. Scandinavian Journal of Statistics, 2004, 31(4), pp. 515-534.
[11] De Boor C. A practical guide to splines. Springer. New York. 1978, pp. 168-203.
[12] Brown L D, Levine M. Variance Estimation in Nonparametric Regression via the Difference Sequence Method.The Annals of Statistics. 2007, 35(5), pp. 2219—2232.
[13] Cai T T, Levine M, Wang L. Variance Function Estimation in Multivariate Nonparametric Regression with Fixed Design.Journal of Muhivariate Analysis. 2009, 100(1), pp. 126—136.
[14] Huang, J. Z, Shen. H. P. Functional Coefficient Regression Models for Non-linear Time Series: A Polynomial Spline Approach. Scandinavian Journal of Statistics.2004, 31(4), pp. 515-534.
[15] Wu X Q, Tian Z, Li X B. Spline Estimates in Functional-Coefficient Linear Autoregressive Models. Journal of Mathematical Reseach and Exposition. 2007, 27(4), pp. 869-875.
[16] Stone, C. J., Hansen, M., Kooperberg, C. & Truong, Y. Polynomial splines and their tensor products in extended linear modeling (with discussion). The Annals of Statistics. 1997, 25, pp. 1371– 1470.
[17] Huang, J. Z. Projection estimation in multiple regression with applications to functional ANOVA models. The Annals of Statistics. 1998, 26, pp. 242 – 272.
[18] Huang, J. Z. Concave extended linear modeling: a theoretical synthesis. Statist. Sinica. 2001, 11, pp. 173– 197.
[19] Liu H B, Liu L. Analysis on the Influencing Factors of CPI Based on VAR Model. Journal of Yunnan University of Finance and Economics. 2009, 1, pp. 119-124.

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