建构区域宏观经济景气指标体系的灰色方法

【作者】 赵保胜；

【导师】 田建国；

【作者基本信息】 山东师范大学 ， 应用数学， 2003， 硕士

【摘要】 宏观经济景气及预警分析是根据经济运行中体现出来的统计规律，运用计算机技术对经济波动进行分析和监测预警的一套有效方法。随着经济改革的不断深入和市场经济体制的确立，宏观经济监测与预警系统的实用研究在我国逐步得到了广泛开展，国家统计局及大多省份都推出了自己的预警系统。建立宏观经济景气指标体系是实现对宏观经济监测与预警的前提和基础。本论文对建构区域宏观经济景气指标体系的方法进行了探讨。 文中分析了现行景气指标分类法在建构区域宏观经济景气指标体系中的局限性，将灰色系统方法引入到区域宏观经济景气指标的分类中，创建了灰色趋势关联度分析法，并将趋势关联度引申到灰色聚类中，以辅助建立区域宏观经济指标体系。 一、灰色关联度及其存在问题探讨 1、常见关联度存在的缺陷。见于应用的灰关联度有：一般关联度，绝对关联度，相对关联度，斜率关联度。文中指出，一般关联度存在下列缺陷：①关联序与初值化的方法有关；②关联序与分辨系数有关；③不满足规范性；④只能体现正关联，难以体现负关联关系。绝对关联度、相对关联度及斜率关联度尽管作了一些改进，但仍不满足规范性的要求，不能体现负关联关系。 2、灰色关联度存在缺陷的原因。这既与关联度的计算方法有关，同时也与以下因素有关：曲线相似性的定义、规范性的约定及初值化的方法。 3、运用灰色关联分析法将区域宏观经济景气指标分类时，应考虑以下3个问题：（1）同类指标具有相同或最相近的发展态势；（2）选用的关联度既要反映正关联，也要反映负关联关系；（3）选用的关联度应满足规范性。 二、时差灰色趋势关联度 介绍了灰色统计的基本思想。给出了趋势关联度的定义以及区域宏观经济景气指标分类的时差趋势关联度分析法。 定义1 设时间序列X₀=（x₀（1），x₀（2），…，x₀（n））， x₁=（x₁（1），x₁（2），…，x₁（n））， 令Δx₀（k+1）=x₀（k+1）-x₀（k），Δx₁（k+1）=x₁（k+1）-x₁（k），若Δx₀（k+1）·Δx₁（k+1）≥0，k=1,2,…,n-1，则称序列x₀、x₁具有相同的发建构区域宏观经济景气指标体系的灰色方法展态势;若公。（k+l）·故1（k+1）<0，k==1，2，…，n一1，称序列X。、Xl对弈。 定理1序列x与Y=aX+C，（a>0具有相同的发展态势。 定义2设Xo=（x。（1），xo（2），…，xo（n））常值序列e=（c，。，…，。），e为实数），X，=（xi（1），x，（2），…，x，（n））为一长度相同的1一时距序列i=1，2，…，m，lx。（k+1）一x。（k）}护0·月一l艺Ix，（k+1）一x，（k）l‘0k=l曰艺k=l 且令:D，=六薯，一‘“·‘，一‘才‘“”=0，l，2，…，mk=1，2，…，n:=0，1，2，…，m 、l声 k 了砚、 :且 X1一从 一一y，（k）Ay，（k+l）=y，（k+1）一y，（k） k=l，2，一，n一1，i=0，1，2，…，m，sgn!匆。（k+l）·妙，（k+l）】·}帆（k+l）{+!匀，（k+l）}Zmax（}匆。（k+l）}，}奴（k+l）1）Ay。（k+1）·细，（k+l）笋0委（k+l）=Ay0（k+l）·奴（k+l）=0则称:r（x。，X，）= i梦;，（、+1）为x。n一1份弋一’- 丹‘‘l、X，的灰色趋势关联度，否，（k+l）为XO相对于X，在k+1点的关联系数。 定理2灰色趋势关联度具有如下性质: （1）r（X。，X，）。l一l，l]，当r（X。，X，）<0时，X。与Xs负关联; （2）对称性r（X，，XZ）=r（XZ，XI）;（3）惟一性; （4）规范性一l‘r（Xo，X，）‘l，厂（Xo，X，）=l骨X，=aX。+C，其中 a>0，C为常值序列。 （5）灰色趋势关联度反映了时间序列的发展态势的接近程度，两序列的发展态势愈接近，其趋势关联度就越大，反之亦然。灰色趋势关联度与曲线的形状以及其空间位置无关。这正是宏观经济指标分类之所需。建构区域宏观经济景气指标体系的灰色方法三、时差趋势关联度分析法设基准指标为X。=（x。（l），x。（2），…，二。（n）），被选指标为:x‘=（二‘（1），x‘（2），…，x，（n））i二1，2，…，m，且皆为长度相同的1一时距序列，将时差引入其趋势关联度中，得时差灰色趋势关联度，即:心卫，J曰1月、名k了z（X。，Xi）= 1犯一1条_，（k+l）为X。，Xi的时差灰色趋势关联度。式中l为时差或延迟数。rr=maxrl，反映了被选指标与基准指标的时差相关关 一乙女三L系，相应的延迟数r表示超前或滞后期。 四、将趋势关联度引申到灰色聚类分析中，得到灰色趋势关联度聚类法，用以辅助时差灰色趋势关联度分析法对区域宏观经济景气指标分类。 五、在实证分析中，运用时差趋势关联度分析法与时差相关系数分析法、峰谷对应法建立了济南市宏观经济景气指标体系，并对指标体系的经济意义进行了分析。更多还原

【Abstract】 The macroscopic economic prosperity and early warning analysis is a set of effective method which, with computer technology, analyzes, monitors and early warns the economic fluctuation according to the statistic law reflected in economic cycling. With the further development of economic reform and the establishment of market economic system, the applied research of macroscopic economic monitoring and early warning system has been spread step by step in China. The National Statistic Bureau and most provinces have set up their own early warning system. To establish the index system of macroscopic economic prosperity is the premise and base of realizing the macroscopic economic monitoring and early warning. This thesis discusses the methods of constructing the index system of regional macroscopic economic prosperity.The thesis analyzes the limitations of the current classified index method of prosperity which has been applying in constructing the index system of regional macroscopic economic prosperity; introduces gray system method to the classified index of regional macroscopic economic prosperity; and establishes the analytic method of the gray trendy degree of incidence. Furthermore, the thesis applies the gray trendy degree of incidence in gray clusters to help the construction of the index system of regional macroscopic economic prosperity.I. The Investigations on the Gray Trendy Degree of Incidence and its Problems.1. The Defects of Common Used Degrees of Incidence.The applied gray degrees of incidence include: general degree of incidence, absolute degree of incidence, relative degree of incidence and slope degree of incidence. The defects of general degree of incidence are: 1) the incidence order relating to the method of initial valuation; 2) the incidence order relating to resolution ratio; 3) unsatisfying the norms; 4) only reflecting the direct incidence, but not the negative incidence. Though absolute degree of incidence, relative degree of incidence and slope degree of incidence have improved a lot, yet they haven’t satisfied the norms and couldn’t reflect the negative incidence.2. The Reasons of the DefectsThe reasons relate to both the calculating method of the degree of incidence and the following elements: the definition of curve similarity, the agreement of the norms and the method of initial valuation.3. Three aspects should be considered when applying gray incidence analytic method to the classified index of regional macroscopic economic prosperity:1) the similar indicators have the same or most similar developing situation; 2) the degree of incidence chosen should reflect both the direct incidence and the negative incidence; 3) the degree of incidence chosen should satisfy the norms.II. Time Difference Gray Trendy Degree of IncidenceThis part tries to introduce the fundamental thought of gray statistics. Then it defines the trendy degree of incidence and the analytic method of time difference trendy degree of incidence on classified index of regional macroscopic economic prosperity.Definition 1: Let time sequence: X0 = (x0(1),x0(2),...,.x0(n)),If ,then sequences X0 and X1 have the same developing situation; if then sequences X0 and X1 "play chess".Theorem 1: Sequence X and F = aX + C ( a > 0 , constant sequence C = (c,c,...,c) , c is a real number) have the same developing situation.Definition 2: Letone-unit time sequence, andThen is X0 and xi.’s gray trendy degree of incidence, (k + 1) is x0 ’s incidence coefficient to x, on the point of k + 1 .Theorem 2: Gray trendy degree of incidence has the following characters:1) , X0and Xt are negative incidence;2) Symmetry: 3) Uniqueness;4) Norms: , among which, a>0,C is a constant sequence;5) Gray trendy degree of incidence reflects the close degree of the developing situation of time sequences, the closer of the developing situation of these two sequences, the greater of the trendy degree of incidence, and vive versa. Gray trendy degre更多还原