The Parameter Estimates Of Fuzzy Linear Regression Model And The Application In Finance

The linear regression analysis is one of the most useful methods in applications such as Engineering, Society , Economy and Finance field. Nowadays the classical statistic theory has been already quite perfect, the classical regression is always limited to accurate data-processing, however in real life the observations are fuzzy data, so the fuzzy data- processing becomes a new research field.With the development of the Fuzzy sets theory, fuzzy regression got its foundation. Since Tanaca put forward the first fuzzy linear regression model in 1982, many specialists have devoted themselves to the fuzzy regression research, and made quiet a few achievements. Such problems are still remained as follows: At present the research of the fuzzy regression almost focuses on the triangular fuzzy data ,which limits the applications of the model;How to value the different models acquired with the different metric by the means of the least- squares method;Few application of the fuzzy regression is founded in the financial field, so it is essential to initiate these research..The study of this paper mainly includes two aspects: The parameter estimates of the trapezoidal fuzzy linear regression model and the application in the company valuation. The least square regression of the fuzzy linear model is developed to deal with the linear models with trapezoidal fuzzy observation data and crisp coefficients. The existence of the estimation of regression coefficients is proved. For single variable linear regression analytical formulations are derived directly. Moreover, the multiple linear regression is converted to a quadric programming. The example demonstrates the methods are applicable. As to the second part: the application in the company valuation, The fuzzy regression technology is introduced to the classicalfinancial valuation models. Because of their influence on the stock price, some representative indexes are chosen and translated to trapezoidal fuzzy data, so a fuzzy multiple-factors valuation model is derived to decide the stocks' intrinsic value.That the new metric is introduced to trapezoidal Fuzzy data space to discuss the parameter estimates of the trapezoidal fuzzy linear regression model broadens the model's application and has universal significance;Compared to the original valuation models, the classical financial valuation models combined with the fuzzy regression technology makes the valuation result more accurate and reliable.* Wang Lijun (Applied Mathematics) Supervised by Feng Yuhu...