经济预测季节变动

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,第六章 季节变动预测法,平均数趋势整理法,趋势比率法,环比法,季节变动,:,由于自然条件和社会条件的影响,经济现象在一年内随季节的转变,而引起的周期性变动,进行季节变动的分析和预测,应判断该时间序列,是否呈周期性变动,一般可按三至五年的已知资,料绘制历史曲线图来判断其在一年内有无周期性,波动,平均数趋势整理法,平均数趋势整理法:,先对历史资料各年同月或同季的数据求平均数,然后,再利用所求出的平均数,消除其中的趋势成分,求出季,节指数,最后建立趋势季节模型进行预测的方法,设有一时间序列,T为序列长度,这一序列是由N(N大于等于3)年的统计资料构成,它受直线,趋势,季节变动和随机变动的影响.若一年季节周期的分段,为k,则N*k=T,现以月为单位,则k=12,T=12N,具体步骤如下:,1 求各年同月的平均数,2 求各年的月平均,3 建立趋势预测模型,根据年的月平均数,建立年趋势直线模型,其中t是以年为单位,用最小平方法估计参数,a,b,并取序列,的中点年为时间原,点.再把此模型转变为月趋势直线模型,分别为新原点（7月份)的月趋势值和每月增量,利用此月趋势直线模型求原点年各月份的趋势值,可得到,4 求季节指数,先计算同月平均数与原点年该月的趋势值的比值,再消除随机干扰,经过修正后可得到季节指数,为修正系数,5 求预测值,首先,用月趋势直线模型求未来月份的趋势值:,然后再用趋势季节模型求其预测值,已知某市19881990年某商品销售量如表,用平均数趋势整理法预测1991年1至3月该商,品销售量,年,1,2,3,4,5,6,7,8,9,10,11,12,合计,月平均,1988,5,3,12,9,13,20,37,44,26,14,5,1,189,15.75,1989,3,13,18,19,31,34,60,62,56,24,8,2,330,27.50,1990,9,15,31,37,42,51,90,98,80,40,11,4,508,42.33,合计,17,31,61,65,86,105,187,204,162,78,24,7,1027,85.58,同月平均,5.67,10.33,20.33,21.67,28.67,35.00,62.33,68.00,54.00,26.00,8.00,2.33,342.3,28.53,各月趋势值,22.43,23.54,24.65,25.76,26.86,27.97,29.08,30.19,31.30,32.41,33.51,34.62,28.53,比值,25.28,43.88,82.47,84.12,106.74,125.09,214.34,225.24,175.52,80.22,23.87,6.73,1190.5,季节指数,25.48,44.23,83.13,84.79,107.59,126.09,216.05,227.04,173.90,70.86,24.06,6.78,1200,月,年,1,2,3,4,5,6,7,8,9,10,11,12,合计,月平均,1988,5,3,12,9,13,20,37,44,26,14,5,1,189,15.75,1989,3,13,18,19,31,34,60,62,56,24,8,2,330,27.50,1990,9,15,31,37,42,51,90,98,80,40,11,4,508,42.33,合计,17,31,61,65,86,105,187,204,162,78,24,7,1027,85.58,同月平均,5.67,10.33,20.33,21.67,28.67,35.00,62.33,68.00,54.00,26.00,8.00,2.33,342.3,28.53,各月趋势值,22.43,23.54,24.65,25.76,26.86,27.97,29.08,30.19,31.30,32.41,33.51,34.62,28.53,比值,25.28,43.88,82.47,84.12,106.74,125.09,214.34,225.24,175.52,80.22,23.87,6.73,1190.5,季节指数,25.48,44.23,83.13,84.79,107.59,126.09,216.05,227.04,173.90,70.86,24.06,6.78,1200,月,年份,年次(,t),销量,1988,-1,15.75,-15.75,1,1989,0,27.75,0,0,1990,1,42.33,42.33,1,合计,0,85.58,25.68,2,t,以年为单位,t,以年为单位,计算原点年(1989)各月的趋势值,每月的增量,当t0,代表原点年中点（6月下半月至7月上半月）的趋势值,6月的趋势值=28.53-0.554=27.98,7月的趋势值=28.53+0.554=29.08,为简便计算可将原点改为7月,t,以月为单位,计算季节指数,先计算同月平均数与原点年该月的趋势值的比值,再消除随机干扰,经过修正后可得到季节指数,为修正系数,=1200/1190.5=1.008,求预测值,趋势比率法,趋势比率法:,:,根据历史上各期的实际值,首先建立趋势预测模型,求历史上各期的趋势值,然后以实际值除以趋势值,进行同月（季）平均,计算季节指数,最后用季节指数和趋势值结合来求预测值的方法.,预测步骤:,建立趋势预测模型求历史上各期的趋势值,求趋势值季节比率,各实际值与相应时期趋,势值的比值,求季节指数,即把同期趋势季节比率平均,建立趋势季节模型进行预测,例:已知某商品4年来各季节商品销售量如下表,预测下年各季的销售量,季度,一,二,三,四,一,二,三,四,一,二,三,四,一,二,三,四,合计,平均,季顺序,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,136,8.5,销售量,15,19,7,10,16,20,8,11,16,22,9,12,19,25,15,18,242,15.125,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,1496,15,38,21,40,80,120,56,88,144,220,99,144,247,350,225,288,2175,b=(nt*Yt-tYt)/nt-(t),a=(Yt/n)-(bt/n),求历史各期的趋势值,.,.,年,季,季顺序,实际销量,趋势值,趋势季节比率,1987, 1,1,15,12.52,119.81,2,2,19,12.87,147.63,3,3,7,13.22,52.95,4,4,10,13.56,73.75,1988, 1,5,16,13.91,115.03,2,6,20,14.26,140.25,3,7,8,14.60,54.79,4,8,11,14.95,73.58,1989, 1,9,16,15.30,104.58,2,10,22,15.65,140.58,3,11,9,15.99,56.29,4,12,12,16.34,73.44,1990, 1,13,19,16.69,113.84,2,14,25,17.03,146.80,3,15,15,17.38,86.31,4,16,18,17.73,101.52,年,第一节度,第二季度,第三季度,第四季度,合计,1987,119.81,147.63,52.95,73.75,394.14,1988,115.03,140.25,54.79,73.58,383.65,1989,104.58,140.58,56.29,73.44,374.89,1990,113.84,146.80,86.31,101.52,448.47,合计,453.26,575.26,250.34,322.29,1601.15,同季平均,113.32,143.82,62.59,80.57,400.3,季节指数,113.24,143.71,62.54,80.51,400,修正系数=400/400.3=0.99925,进行预测,预测模型为,环比法,环比法(帕森斯法):,根据历年(至少三年)各月或各季的历史资料,逐期计算环比并加以平均,求出季节指数进行预测的方法.,预测步骤为:,求各期的环比(将各期的实际值除以前期的实际值),求各年相同的平均环比,求连锁系数(任选一期为基准期,其连锁系数为1),然后根据公式,根据趋势变动修正连锁系数,如果数据没有趋势变动,所选的基准期的连锁系数应为1.,若求出的基准期的连锁系数,C1,不为1,则表示存在趋势变动,的影响,应加以修正.设每期连锁系数受到的影响为,则,假定趋势是直线型,个其所受的影响是累加的.个其扣除,后,的修正连锁系数 应为,求季节指数,将各期的修正连锁系数除以修正连锁系数的平均数,计算季节指数,进行预测,例:某地百货公司某种商品各季销售量如下,1,2,3,4,合计,平均,1987,400,900,500,800,2600,650,1988,500,1000,700,1100,3300,825,1989,600,900,700,1300,3500,875,1990,800,1200,900,1400,4300,1075,求1991年各季度的需求量,1,2,3,4,实 1987,400,900,500,800,际 1988,500,1000,700,1100,值 1989,600,900,700,1300,1990,800,1200,900,1400,环 1987,2.25,0.56,1.60,1988,0.63,2.00,0.70,1.57,比 1989,0.55,1.50,0.78,1.86,1990,0.62,1.50,0.75,1.56,平均环比,0.6,1.81,0.70,1.65,连锁系数,1(1.254),1.81,1.267,2.09,修正连锁系数,1.000,1.747,1.140,1.900,季节指数,0.691,1.207,0.788,1.313,年份,年次(,t),季平均销售量,1987,-3,650,-1950,9,1988,-2,825,-825,1,1989,1,875,875,1,1990,3,1075,3225,9,合计,0,3425,1325,20,练习题,某商品三年的需求量个季数据如下,1,2,3,4,1,190,617,1570,580,2,363,1070,1750,96,3,38,1300,1580,74,年,季,用平均数趋势整理法求下年各季的需求量,某地火车站运送乘客三年来各季数据如下,1,2,3,4,1,169,80,113,89,2,133,72,117,85,3,140,82,128,87,年,季,用趋势比率法求下年第一季度的客运量,某市某产品四年的销量如下,1,2,3,4,1,1000,800,1300,1100,2,1200,1000,1500,1200,3,1000,900,1900,1200,4,1300,1100,1800,1300,季,年,用环比法求下年各季的销售量,