二次曲线指数平滑法课件

,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,2011/3/23,#,二次曲线指数平滑法,二次曲线指数平滑法,1,时间序列平滑预测法回顾,一次移动平均法,一次指数平滑法,线性二次移动平均法,线性二次指数平滑法,二次曲线指数平滑法,时间序列平滑预测法回顾一次移动平均法,2,几种方法的比较,一次移动平均法,一次指数平滑法,几种方法的比较一次移动平均法一次指数平滑法,3,有明显的线性变化趋势时,用线性二次移动平均法,线性二次指数平滑法,有明显的线性变化趋势时,4,二次曲线指数平滑法,应用背景：,有的时间序列虽然有增加或减少趋势，但不一定,是线性的，可能按二次曲线的形状增加而减少。,二次曲线指数平滑法应用背景：,5,基本原理,对于这种非线性增长的时间序列，采用二次曲线指数平滑法可能要比线性指数平滑法更为有效。它的特点是不但考虑了线性增长的因素，而且也考虑了二次抛物线的增长因素。二次曲线指数平滑法的计算过程共分七个步骤。,基本原理,6,1.,计算,t,时期的单指数平滑值,2.,计算,t,时期的双指数平滑值,3.,计算,t,时期的三重指数平滑值,1.计算t时期的单指数平滑值,7,4.,计算,t,时期的水平值,5.,计算,t,时期的线性增量,6.,计算,t,时期 的抛物线增量,4.计算t时期的水平值,8,7.,预测,m,时期以后，即 时期的数值,虽然二次曲线指数平滑法的计算方法比前几种指数平滑法复杂，但对非平稳时间序列的预测相当有效，它能随着时间序列呈抛物线增长而调整预测值。,7.预测m时期以后，即 时期的数值,9,时期水平值的推导,修正的,修正的,修正的,时期水平值的推导 修正的,10,线性增量 的奥秘,线性增量 的奥秘,11,例题,某地区统计了从,19832006,年每年的消费品销售总额，数据如下表，通过计算机求解平滑常数最佳值为,0.5,，此时对应均方差最小，逐年预测，,m=1,，计算结果如下。,例题某地区统计了从19832006年每年的消费品销售总额，,12,预测模型的具体步骤及表达式如下,预测模型的具体步骤及表达式如下,13,t,年度,观测值（,x）,1,1983,12.9,12.9,12.9,12.9,2,1984,14.91,13.905,13.4025,13.15125,14.65875,1.130625,0.25125,3,1985,15.96,14.9325,14.1675,13.65938,15.95438,1.407188,0.256875,15.915,4,1986,14.41,14.67125,14.41938,14.03938,14.795,-0.06844,-0.12813,17.49,5,1987,14.57,14.62063,14.52,14.27969,14.58156,-0.24859,-0.13969,14.6625,6,1988,14.6,14.61031,14.56516,14.42242,14.55789,-0.19879,-0.09758,14.26313,7,1989,15.35,14.98016,14.77266,14.59754,15.22004,0.288457,0.032383,14.31031,8,1990,15.84,15.41008,15.09137,14.84445,15.80059,0.498203,0.071797,15.52469,9,1991,16.9,16.15504,15.6232,15.23383,16.82934,0.887988,0.142461,16.33469,10,1992,18.26,17.20752,16.41536,15.82459,18.20107,1.295637,0.201392,17.78855,11,1993,17.4,17.30376,16.85956,16.34208,17.67468,0.26099,-0.07328,19.5974,12,1994,18.71,18.00688,17.43322,16.88765,18.60863,0.643881,0.028088,17.89902,13,1995,19.53,18.76844,18.10083,17.49424,19.49707,0.820158,0.061019,19.26655,14,1996,20.82,19.79422,18.94753,18.22088,20.76097,1.146825,0.120052,20.34774,15,1997,22.87,21.33211,20.13982,19.18035,22.75723,1.774355,0.232825,21.96782,16,1998,24.59,22.96105,21.55044,20.36539,24.59725,1.974558,0.225576,24.64799,17,1999,25.93,24.44553,22.99798,21.68169,26.02432,1.775674,0.131251,26.68459,18,2000,28.04,26.24276,24.62037,23.15103,28.0182,2.005012,0.153048,27.86562,19,2001,29.45,27.84638,26.23338,24.6922,29.53122,1.792582,0.071831,30.09974,20,2002,31.47,29.65819,27.94578,26.31899,31.45621,1.926448,0.085617,31.35971,21,2003,33.99,31.8241,29.88494,28.10197,33.91943,2.329612,0.156183,33.42547,22,2004,39.56,35.69205,32.78849,30.44523,39.15589,4.30428,0.560291,36.32714,23,2005,48.08,41.88602,37.33726,33.89124,47.53754,7.305642,1.102751,43.74032,24,2006,53.67,47.77801,42.55764,38.22444,53.88557,7.438329,0.887181,55.39456,25,2007,61.76749,t年度观测值（x）1198312.912.912.912.9,14,二次曲线指数平滑法课件,15,二次曲线指数平滑法课件,16,二次曲线指数平滑法课件,17,二次曲线指数平滑法课件,18,二次曲线指数平滑法课件,19,二次曲线指数平滑法课件,20,Thank you,Thank you,21,