Fuzzy Varying Coefficient Bilinear Regression of Yield Series
Affiliation(s)
College of Science, University of Shanghai for Science and Technology, Shanghai, China.
College of Science, University of Shanghai for Science and Technology, Shanghai, China.
ABSTRACT
We construct a fuzzy varying coefficient bilinear regression model to deal with the interval financial data and then adopt the least-squares method based on symmetric fuzzy number space. Firstly, we propose a varying coefficient model on the basis of the fuzzy bilinear regression model. Secondly, we develop the least-squares method according to the complete distance between fuzzy numbers to estimate the coefficients and test the adaptability of the proposed model by means of generalized likelihood ratio test with SSE composite index. Finally, mean square errors and mean absolutely errors are employed to evaluate and compare the fitting of fuzzy auto regression, fuzzy bilinear regression and fuzzy varying coefficient bilinear regression models, and also the forecasting of three models. Empirical analysis turns out that the proposed model has good fitting and forecasting accuracy with regard to other regression models for the capital market.
We construct a fuzzy varying coefficient bilinear regression model to deal with the interval financial data and then adopt the least-squares method based on symmetric fuzzy number space. Firstly, we propose a varying coefficient model on the basis of the fuzzy bilinear regression model. Secondly, we develop the least-squares method according to the complete distance between fuzzy numbers to estimate the coefficients and test the adaptability of the proposed model by means of generalized likelihood ratio test with SSE composite index. Finally, mean square errors and mean absolutely errors are employed to evaluate and compare the fitting of fuzzy auto regression, fuzzy bilinear regression and fuzzy varying coefficient bilinear regression models, and also the forecasting of three models. Empirical analysis turns out that the proposed model has good fitting and forecasting accuracy with regard to other regression models for the capital market.
KEYWORDS
Fuzzy Varying Coefficient Bilinear Regression Model, Fuzzy Financial Assets Yield, Least-Squares Method, Generalized Likelihood Ratio Test, Forecast
Fuzzy Varying Coefficient Bilinear Regression Model, Fuzzy Financial Assets Yield, Least-Squares Method, Generalized Likelihood Ratio Test, Forecast
Cite this paper
He, T. and Lu, Q. (2015) Fuzzy Varying Coefficient Bilinear Regression of Yield Series. Journal of Data Analysis and Information Processing, 3, 43-54. doi: 10.4236/jdaip.2015.33006.
He, T. and Lu, Q. (2015) Fuzzy Varying Coefficient Bilinear Regression of Yield Series. Journal of Data Analysis and Information Processing, 3, 43-54. doi: 10.4236/jdaip.2015.33006.
References
[1] Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353.
http://dx.doi.org/10.1016/S0019-9958(65)90241-X [2] Li, Z.-Y., Zhang, C. and Wang, T.-J. (2010) Studying on the Interval Financial Times Series and Evaluating on the Forecast. Journal of Applied Statistics and Management, 29, 129-136. [3] D’Urso, P. and Gastaldi, T. (2000) A Least-Squares Approach to Fuzzy Linear Regression Analysis. Computational Statistics and Data Analysis, 34, 427-440.
http://dx.doi.org/10.1016/S0167-9473(99)00109-7 [4] Li, Z.-Y., Liu, W.-Y. and Wang, T.-J. (2009) Fuzzy Bilinear Regression of Yields Series. Statistical Research, 26, 68-73. [5] Wang, H.-D., Guo, S.-C. and Yue, L.-Z. (2014) An Approach to Fuzzy Multiple Linear Regression Mode Based on the Structured Element Theory. Systems Engineering—Theory & Practice, 34, 2628-2636. [6] Hu, B.-Q. (2010) Foundations of Fuzzy Theory. Wuhan University Press, Wuhan, 103-114. [7] Xu, R.N. (1991) A Linear Regression Model in Fuzzy Environment. Advances in Modelling Simulation, 27, 31-40. [8] Fan, J.Q. and Yao, Q.W. (2003) Nonlinear Time Series. Springer, Berlin, 243-245. [9] Cai, Z.W., Fan, J.Q. and Yao, Q.W. (2000) Functional-Coefficient Regression Models for Nonlinear Times Series. Journal of the American Statistical Association, 95, 941-956.
http://dx.doi.org/10.1080/01621459.2000.10474284
[1] Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353.
http://dx.doi.org/10.1016/S0019-9958(65)90241-X [2] Li, Z.-Y., Zhang, C. and Wang, T.-J. (2010) Studying on the Interval Financial Times Series and Evaluating on the Forecast. Journal of Applied Statistics and Management, 29, 129-136. [3] D’Urso, P. and Gastaldi, T. (2000) A Least-Squares Approach to Fuzzy Linear Regression Analysis. Computational Statistics and Data Analysis, 34, 427-440.
http://dx.doi.org/10.1016/S0167-9473(99)00109-7 [4] Li, Z.-Y., Liu, W.-Y. and Wang, T.-J. (2009) Fuzzy Bilinear Regression of Yields Series. Statistical Research, 26, 68-73. [5] Wang, H.-D., Guo, S.-C. and Yue, L.-Z. (2014) An Approach to Fuzzy Multiple Linear Regression Mode Based on the Structured Element Theory. Systems Engineering—Theory & Practice, 34, 2628-2636. [6] Hu, B.-Q. (2010) Foundations of Fuzzy Theory. Wuhan University Press, Wuhan, 103-114. [7] Xu, R.N. (1991) A Linear Regression Model in Fuzzy Environment. Advances in Modelling Simulation, 27, 31-40. [8] Fan, J.Q. and Yao, Q.W. (2003) Nonlinear Time Series. Springer, Berlin, 243-245. [9] Cai, Z.W., Fan, J.Q. and Yao, Q.W. (2000) Functional-Coefficient Regression Models for Nonlinear Times Series. Journal of the American Statistical Association, 95, 941-956.
http://dx.doi.org/10.1080/01621459.2000.10474284