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).
<p>[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.</p>
<p>[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.</p>
@article{"International Journal of Engineering, Mathematical and Physical Sciences:65341", author = "LI qiu-min and TIAN yi-xiang and ZHANG gao-xun", title = "GMDH Modeling Based on Polynomial Spline Estimation and Its Applications", abstract = "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).
", keywords = "spline, GMDH, nonparametric, bias, forecast.", volume = "7", number = "3", pages = "544-5", }
