时间序列预测PPT学习教案

1、会计学1时间序列预测时间序列预测第1页/共56页第2页/共56页第3页/共56页nxnxxxxxxniin1321.第4页/共56页观察期123456预测值观察值10501080 1030 1070 1050 10601057第5页/共56页1.3211332211nniiinnwwwwxwxwxwxwxwxx其中第6页/共56页观察期123456预测值观察值10501080 1030 1070 1050 10601056权重(w)第7页/共56页nnnnnnnaaaaaaaaaaxxxxxxxx01231201321.或 第8页/共56页观察期0123

2、4567预测值观察值115012101290136013801415147015001558环比速度-105.2106.6105.4101.5102.5103.9102.0第9页/共56页第10页/共56页第11页/共56页nxxxxMxntttttt)1(21)1(1.第12页/共56页观察年份观察年份时时 序序实际观察值实际观察值Mt(1)(n=4)199113819922451993335199444941.75199557049.75199664349.25199774652.00199885553.50199994547.252000106552.752001116457.25200

3、2124354.25第13页/共56页0T第14页/共56页)(122.)2()1()2()1()1()1()1(2)1(1)1()2()1(21)1(ttttttttTtntttttntttttMMnbMMaTbaxnMMMMMnxxxxM其中第15页/共56页观察年份观察年份时时 序序实际观察值实际观察值Mt(1)(n=4)Mt(2)(n=4)199113819922451993335199444941.75199557049.75199664349.25199774652.0048.19199885553.50512550.502000106552.7551.3

4、82001116457.2552.692002124354.2552.88第16页/共56页53.561913.062.55913.062.55913.0)88.5225.54(142)(1262.5588.5225.542211212)2(12)1(1212)2(12)1(1212xTxMMnbMMaT预测2003年所以有第17页/共56页第18页/共56页tttxxx)1(1)1(1221)1(1)1()1(.)1()1()1(tttttttttxxxxSxS第19页/共56页时 序12345678910111213销售量10158201016182022242026St(1)1110.5

5、12.810.415.212.614.322.021.023.55.0第20页/共56页)2(1)1()2()1(tttSSS)(12)2()1()2()1(ttttttttTtSSbSSaTbax其中第21页/共56页观察年份时 序观察值St(1)St(2)199614041.53442.655199724745.90645.256199835653.98152.236199946562.79660.684200057068.55966.984200167573.71272.366200278280.34278.747TTbaxSSbSSaT38.6937.8138.

6、6)747.78342.80(8 .018 .0)(1937.81747.78342.8022777)2(7)1(77)2(7)1(778 . 0第22页/共56页)3(1)2()3()2(1)1()2()1(1)1()1()1()1(tttttttttSSSSSSSxS第23页/共56页)2()1 (2)34()45(2)56()1 (233)3()2()1(22)3()2()1()3()2()1(2tttttttttttttttTtSSScSSSbSSSaTcTbax其中第24页/共56页第25页/共56页111212tbxattxxbbtax其中)、(2211,),(txtx第26页/共

7、56页观察年份199419951996199719981999200020012002时 序123456789观察值131516181921232426预测值2003（25.5）第27页/共56页tbtaxtbxattxxbttxx56.1555.235.7498765.2443215.234262423215.154181615131112122121第28页/共56页2ctbtax233322222111tctbaxtctbaxtctbaxacb、第29页/共56页观察年份199719981999200020012002时 序1234

8、56观察值1200140016201862212724135 . 526522702241321275 . 324317412186216205 . 12211300214001200332211txtxtx 第30页/共56页2222115 .16525.1024115 .16525.10245 . 55 . 522705 . 35 . 317415 . 15 . 11300ttxcbacbacbacba所以有 求解得第31页/共56页tbxtbxnattnxttxnbbtax)(1)(22其中第32页/共56页观察年份时 序(t)观察值(x)txt2趋势值199311313112.7199

9、421530415.5199531854918.21996420801620.919975241202523.619986271623626.319997302104929.120008322566431.820019353158134.62002103636010037.3合计2501600385250第33页/共56页tbtaxtbxtbxnattnxttxnbt txnxxntt727.210105.5727.225)(1727.28252250553851025055160010)(385160025102505.510552222 第34页/共56页T)t (MRtM,33 和 ),

10、1(1btaxbRanRTbbnaTbaR3115)34(311即有第35页/共56页T)t (MRtM, 和 ),(3311bRanRTbbnaTbaR373)32(37即有第36页/共56页观察年份时序t观察值x权数wwx加权平均199314.4014.40R199424.7829.56199535.13315.39199645.81合计29.354.89199756.94199867.36加权平均199978.1318.13T200088.56217.12200198.91326.73合计51.988.66第37页/共56页txbRanRTbxxxTxxxR63.042.342.363.

11、03789.43763.03989.466.8366.8)32(321189.4)32(3211987321所以有即有第38页/共56页),(11RtM),( 和 ),(3322TtMStM2ctbtax第39页/共56页cbRacnnRTbnSTRccnbnaTcnbnaScbaR153113735)5()2(2)34()34()673(673)311(3112222即有第40页/共56页cbRacnnRTbnSTRccnbnaTcnbnaScbaR6373533)3()2(2)32()32()653(653)37(372222即有第41页/共56页观察年份时 序(t)观察值(x)权数wwx

12、加权平均1992141141R1993251210219943593177199546632053.31996572172S1997677215419987823246199988547278.72000986186T200110852170200211823246合 计50283.7第42页/共56页2226375.0875.11625.29625.29)6375.0(6875.11373 .53637875.11)6375.0(351133113 .537 .8335336375.0)311()7 .7827 .833 .53(2)3()2(27 .837 .783 .53ttxcbRac

13、nnRTbnSTRcTSR所以有即有 第43页/共56页第44页/共56页第45页/共56页%100XxSIiiixX第46页/共56页月 年199920002001合计月平均季节指数预测值18012032052017313.7342.5212020040072024019.04753200350700125041733.1827.545008501500285095075.31882.558001500240047001567124.33107.56250045006800138004600364.891207240064007200160005333422.910572.586009001

14、5003000100079.31982.59200400600120040031.7792.51010025040075025019.849511601002003601209.5237.5124080110230776.1152.5合计760015650221304538012611200.002500第47页/共56页第48页/共56页观察年分时序（t）观察值（x）t2tx趋势值趋势比率（TI）199913213225.091.2821843626.210.6932196327.330.774391615628.451.3720005362518029.371.226213612630.6

15、90.687244916831.810.758446435232.931.3420019398135134.051.15102510025035.170.71112812130836.290.77124814457637.411.28合计783756502598第49页/共56页btaxt97.23127812.11237512.1786501237578259812)(222 ntbnxattnxttxnbtxt12.197.23第50页/共56页89.411612.197.2377.401512.197.2365.391412.197.2353.381312.197.2381.31712.

16、197.2321.26212.197.2309.25112.197.2316151413721xxxxxxx第51页/共56页28. 141.374877. 029.362877. 033.272169. 021.261828. 109.2532121212111111333222111xxTIxxTIxxTIxxTIxxTIxxTIiii所以有 :趋势比率的计算公式是第52页/共56页33.1376.0377.075.077.069.0371.068.069.022.134321SISISISI第53页/共56页7 .5533. 189.41)(0 .3176. 077.40)(4 .2769. 065.39)(0 .4722. 1