我国人口出生率自相关函数的代际影响数学模型  

Mathematical Modeling of Intergenerational Influence for Fertility Autocorrelations Function in China

作　　者：李建华 吴宗敏[2] LI Jianhua;WU Zongmin(School of Mathematics and Statistics,Hexi University,Zhangye,Gansu 734000,China;School of Mathematics Science,Fudan University,Shanghai 200433,China)

机构地区：[1]河西学院数学与统计学院,甘肃张掖734000 [2]复旦大学数学科学学院,上海200433

出　　处：《数学建模及其应用》2020年第4期28-36,共9页Mathematical Modeling and Its Applications

基　　金：甘肃省高等学校创新能力提升项目(2020B-215);河西学院校长科研创新基金项目(XZ2020006)。

摘　　要：根据"代际影响的数学模型"中的思想,即大量应用中的时间序列,其跨时间相关性往往呈现出某种周期性质,对我国1949—2019年的出生率数据fj(j=0,1,…,70),人口出生率自相关统计量σ(k)建立了模型:σ*(t)=[A+(1-A)cos(2πt/P)]e-λt2.利用最小二乘法找到了模型的参数A、λ和P.实验表明,该模型对我国1949—2019年4个阶段的出生率自相关函数有很好的反映.通过分析各阶段的模型参数得出:生育周期P的周期性变化及总体呈逐渐缓慢拉长趋势;大趋势衰减因子λ呈明显的递增趋势,从而影响广度σ逐渐缩短.随着社会影响对家庭格局的冲击,人们的生育思想越来越自由,越来越不受前人影响.According to the idea proposed in"mathematical model of intergenerational influence",the autocorrelation function possesses some periodic phenomena.We use the data fj(j=0,1,…,70)and the autocorrelation statistics of birth rate after the liberation of China(1949-2019)to establish mathematical model:σ*(t)=[A+(1-A)cos(2πt/P)]e-λt2.The parameters of the model A,λ,Pare found by using the least square method,and the experiments indicate that the model can reflect the autocorrelation function of birth rate in four stages of China(1949-2019)satisfactorily.By analyzing the model parameters of each stage,we come to the conclusion that the fertility cycle P changes periodically,and in general,it is gradually and slowly lengthened.The attenuation factor of the general trend obviously increase,thus the influence breadth is gradually shortened.With the impact of social influence on the family pattern,people’s thought of giving birth is less influenced by their predecessors,and is becoming more and more individually and freely.

关 键 词：自相关函数 代际周期衰减 牛顿下降法 最小二乘法 交叉检验 

分 类 号：O29[理学—应用数学]