金融区间序列分析及其预测的初步评价  

Studying on the Interval Financial Time Series and Evaluating on the Forecast

作　　者：李竹渝[1] 张成 王泰积[1] 

机构地区：[1]四川大学数学学院,四川成都610064 [2]上海财经大学会计学院,上海200433

出　　处：《数理统计与管理》2010年第1期129-136,共8页Journal of Applied Statistics and Management

基　　金：国家社会科学基金统计学项目(07BTJ003)

摘　　要：金融市场中的实际观测数据,除随机性外往往还带有模糊性,这样的观测数据通常以观测区间的形式给出,例如,当我们谈及某日的上证指数时,其观测值总是在最低点与最高点之间波动。观测值的这种不确定性来自于多重隶属现象,而非随机现象,我们称这种不确定性为模糊性。不确定性问题通常含有两种意义上的分类:一类是随机不确定性,人们依靠概率统计方法进行处理;另一类是非随机性的不确定性,即为模糊性问题,通常利用模糊集合理论来进行研究。本文将在模糊数学理论基础上,利用回归分析方法,构建模糊金融时间序列模型,并利用FLP(模糊线性规划)方法来估计模型的未知参数。为了合理评价拟合效果,我们将根据测量模糊集合间的择近原则,给出利用样本平均贴近度来评价模型拟合效果的一个准则。实证研究将讨论金融模糊时间观测序列的建模、参数估计,并对模型的实际拟合效果和预测效果做初步评价。The real data in financial markets is not only random but often fuzzy. Such data is usually given in the form of observation interval, for example, when we talk about the Shanghai composite index of a certain day, the value of its observation is always between the lowest point and the highest and fluctuates. Observations of this uncertainty that we called fuzzy, comes from the phenomenon of multiple membership rather than random phenomenon. Uncertainty usually contains two kinds of sense： One is random uncertainty, people use the probability and statistics method to deal with; The other is non- random one, actually called fuzzy problem, usually studied with fuzzy set Theory. This paper will be based on fuzzy theory, then construct fuzzy financial time series model by regression analysis, and use FLP （fuzzy linear programming） method to estimate the unknown parameters. In order to evaluate the fitting results reasonable, the principle been used to evaluate the effect of the fitting model by Sample Average of the Closeness, is developed on the basis of the closeness principle of fuzzy sets. Empirical studies will discuss the financial fuzzy time observation series, parameter estimation; and evaluate the results of actual fitting and projecting preliminarily at the same time.

关 键 词：金融区间序列 模糊线性规划 样本平均贴近度 拟合原则 

分 类 号：O212[理学—概率论与数理统计]