基于切比雪夫最佳逼近意义下的CPI指数变化通道的原理与方法
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引用本文:顾乐民.基于切比雪夫最佳逼近意义下的CPI指数变化通道的原理与方法[J].经济数学,2015,(3):54-59
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作者单位
顾乐民 (同济大学 材料科学与工程学院上海200092) 
中文摘要:中国2000-2015年的186组CPI指数所体现的变化规律,可以用通道原理来描述.通道类似于交通图中的道路,依据切比雪夫最佳逼近原理,以CPI函数为中心线,以极小化最大正负误差为边界线,包含了所有的CPI数据,是一条具有最大安全范围意义的数据通道.假设端点数据是建立在零误差基础上的最大权重数据,未来短期内CPI指数的变化不存在突变,或存在突变但其误差不大于通道内的最大正负误差,则通道的延伸可以预测未来CPI指数的变化,以及变化的波动范围.介绍了CPI通道的基本原理与方法、适用范围、判别法则、具体算法等.通过多个数据处理实例,说明了直线通道具有简单易懂、直观性强、计算方便、适用范围广、符合性较好等特点,验证了未来短期CPI指数变化基本是可知与可控的.
中文关键词:切比雪夫  最佳逼近  零误差型极小极大逼近  CPI指数  CPI通道
 
Principle and Method of CPI Index Change Channel Based on Chebyshev Optimal Approximation Significance
Abstract:The 186 sets of CPI index data from 2000 to 2015 years in China reflected some rules, which can be described by Channel principle and the corresponding method. Channel is a data channel with the largest security sense,which based on Chebyshev approximation theory,to the CPI function as its center line, to minimize the maximum positive and negative error as its boundary line,and contains all the CPI data.Assuming that the endpoint data is the largest weight data based on zero error, there is no mutation of CPI index in the short term, or mutation but the error is less than channel's maximum positive and negative error,then the future CPI index can be given by the channel through the forecast value and fluctuation value.This article introduced the CPI channel principle and its method, the applicable scope, the judging rules,the concrete algorithm, etc.Through some examples of data processing, this paper shows that the straight line channel is easy to understand, intuitively simple and strong, convenient in the computation, broad in the applicable scope, good in the compliance, and also verifies that the scope of future short-term changes in the CPI index is knowable and controllable.
keywords:Chebyshev  optimal approximation  zero-error type of minimax approximation  CPI index  CPI channel
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