ARIMA模型預(yù)測(cè)

1、5ARIMA模型預(yù)測(cè)5J模型選取u前，學(xué)術(shù)界較為成熟的預(yù)測(cè)方法很多，各種不同的預(yù)測(cè)方法有其所面向的特定對(duì)象，不存在一種普遍最好”的預(yù)測(cè)方法。GM(1,1)模型預(yù)測(cè)是以灰色系統(tǒng)理論為基礎(chǔ)，通過(guò)原始數(shù)據(jù)的分析處理和建立灰色模型，對(duì)系統(tǒng)未來(lái)狀態(tài)作出科學(xué)的定量預(yù)測(cè)的一種方法。我們采用GM(1,1)模型是基于以下兩方面的考慮：第一，GM(1,1)模型對(duì)數(shù)據(jù)要求較低，而其他多數(shù)預(yù)測(cè)方法以數(shù)理統(tǒng)計(jì)為基礎(chǔ)，對(duì)樣本量有較高要求。我們用來(lái)做預(yù)測(cè)的數(shù)據(jù)時(shí)序只有14年，預(yù)測(cè)使用GM(1,1)模型較好；第二，GM(1,1)模型的計(jì)算量相對(duì)較小，計(jì)算方法相對(duì)簡(jiǎn)單，適用性較好。5.2模型假設(shè)前提1、假設(shè)未來(lái)望慶地區(qū)經(jīng)濟(jì)發(fā)展

2、基本態(tài)勢(shì)不變：2、假設(shè)未來(lái)中央政府對(duì)重慶實(shí)施的政策方向基本不變；3、假設(shè)未來(lái)不會(huì)出現(xiàn)戰(zhàn)爭(zhēng)、瘟疫及其它不可抗拒的自然或社會(huì)因素。預(yù)測(cè)數(shù)據(jù)來(lái)源預(yù)測(cè)樣本為1997-2008年的重慶市農(nóng)資價(jià)格指數(shù)、化學(xué)肥料價(jià)格指數(shù)、飼料價(jià)格指數(shù)。具體預(yù)測(cè)樣本數(shù)據(jù)如下：表5.119972008年重慶部分農(nóng)資價(jià)格指數(shù)單位：%19971998199920002001200220032004200520062007農(nóng)資105.990.493.296.8100.5103.5102.5109.8106.9101.2110.0化肥93.687.496.597.39&999.7101.0106.3108.399.9102.2

3、飼料96.691.091.995.810L1106.6105.6115.7105.5101.1109.2為提高數(shù)據(jù)預(yù)測(cè)的科學(xué)性，我們以1996年(直轄前)的農(nóng)資價(jià)格為基期，假設(shè)1996年農(nóng)資產(chǎn)品價(jià)格為100元，則以后第，年的農(nóng)資產(chǎn)品價(jià)格訃算公式如下:G.=p100xZ99?xxZf經(jīng)此換算，得到1997-2008年的預(yù)測(cè)樣本。其中，NZJG表示換算后的農(nóng)資，HXFL表示換算后的化肥，SL表示換算后的飼料。具體見(jiàn)下表：表5.219972008年轉(zhuǎn)換后的預(yù)測(cè)樣本單位：元19971998199920002001200220032004200520062007NZJG105.995.789.286.4

4、86.889.892.1101.1108.1109.4120.3HXFL93.681.87&976.876.075.776.581.388.188.089.9SL96.687.980.877.47&283.48&1101.9107.5108.7118.754GM(1J)模型建立與檢驗(yàn)541序列的建立iailfn個(gè)原始數(shù)據(jù)組成的原始序列為X(k)二X(9)，x(9)，,x數(shù)(n)。那么可以得到四個(gè)樣本原始序列：NZJGX(6)(k)二105.9,95.7,，120.3)；HXFLX(6)(k)二93.6,81.&89.9)；SLxe(k)96.6,87.9,，11

5、&7。542級(jí)比檢驗(yàn)級(jí)別檢驗(yàn)是GM(1,1)建模的數(shù)據(jù)檢驗(yàn)，經(jīng)訃算可得：NZJG級(jí)比序列二0.904,0.932，1.198)；HXFL地區(qū)序列二0.874,0.965,，L200；SL地區(qū)序列二0,910,0.919,-,LI70)：都落在界區(qū)(0.7515,1.3307)內(nèi)。這表明，以上三個(gè)樣本序列均可以進(jìn)行GM(1,1)模型建模。543模型的方程通過(guò)一次累加生成新序列：X（k）二仗，X，則GMd.1）模型相應(yīng)的微分方程為：其中，&稱為發(fā)展灰度，為內(nèi)生控制灰度，它們是方程中重要的參數(shù)。通過(guò)求解微分方程，即可得到預(yù)測(cè)模型。山于GM（1,1）預(yù)測(cè)模型種類較多，我們選取其中較常用

6、的一種如下：通過(guò)測(cè)算，我們得到三組、值和相應(yīng)的四個(gè)擬合預(yù)測(cè)方程如下表表5.3擬合預(yù)測(cè)方程和.值a擬合預(yù)測(cè)方程N(yùn)ZJG-0.04691572.875525Vd)-(1呼9_72.875525)1(-o.(M69丈JL72.875525-0.046915-0.046915HXFL-0.02734869.157548¥山一(936-69.157548).0.02734®*j_69.157548g”-0.027348-0.027348SL-0.05742164.105061v(h-(966-64.105061)C-(.o.o5742i)a十64.105061g”-0.057421-

7、0,057421544后驗(yàn)差檢驗(yàn)后驗(yàn)差檢驗(yàn)包括殘差的方差比（C）和小誤差概率（P）。首先算得知?dú)埐钇骄禐?x1xr1Q-Z£（6）=-L占（Q胛6）.«i-l«77歷史數(shù)據(jù)方差為町二（1/八）卜伙）7其中歷史數(shù)據(jù)平均值為1»乍叫）殘差方差為后驗(yàn)差比值為C呂小誤差概率為尸=/V&（Q-f<0.6745*1經(jīng)計(jì)算，我們同樣得到四組方差比（C）和小誤差概率（P）如下:表54后驗(yàn)差檢驗(yàn)結(jié)果表CPNZJG0.2739161HXFL0.406991SL0.17281根據(jù)下列后驗(yàn)差檢驗(yàn)結(jié)果判別表，我們認(rèn)為四個(gè)模型均通過(guò)了后驗(yàn)差檢驗(yàn)，有較好的預(yù)測(cè)精度。表

8、5.5后驗(yàn)差檢驗(yàn)結(jié)果判別表CP<0.35>0.95好<0.50>0.80合格<0.65>0.70勉強(qiáng)合格>0.65W0.70不合格545相對(duì)誤差檢驗(yàn)經(jīng)過(guò)對(duì)模型進(jìn)行擬合測(cè)算，得到以下四個(gè)相對(duì)誤差表：表5.6NZJGGM(1,1)模型擬合相對(duì)誤差表時(shí)期實(shí)際值擬合值相對(duì)誤差()199895.779.70-16.72199989.283.53-6.362008144.2127.41-11.64平均相對(duì)誤二6.56%表5.7HXFLGM(1,1)模型擬合相對(duì)誤差表時(shí)期實(shí)際值擬合值相對(duì)誤差()199881.872.71-11.12199978.974.72-5.2

9、9表5.8SLGM(1,1)模型擬合相對(duì)誤差表時(shí)期實(shí)際值擬合值相對(duì)誤差()199896.671.69-18.44199987.975.93-6.032008138.8127.30-8.28平均相對(duì)誤差二6.26%2008107.995. 58-11. 42平均相對(duì)誤差二5. 41%綜上分析，我們發(fā)現(xiàn)：以上四個(gè)模型的相對(duì)誤差還是在合理的范ffl內(nèi)，模型可靠，擬合精度較高，可以進(jìn)行預(yù)測(cè)。5.5模型預(yù)測(cè)利用模型預(yù)測(cè)2009-2020年XZJG、HXFL.SL的具體數(shù)值,結(jié)果見(jiàn)表5.9。表5.9GM(1,1)模型預(yù)測(cè)結(jié)果單位：元年份NZJGHXFLSL2009133.598.2134.82010139

10、.9100.9142.82011146.7103.7151.22012153.7106.6160.22013161.1109.6169.62014168.8112.6179.72015176.9115.7190.32016185.411&9201.52017194.3122.2213.42018203.7125.6226.12019213.5129.1239.42020223.7132.7253.6經(jīng)過(guò)換算，我們可以得到2009-2020年重慶市農(nóng)資價(jià)格指數(shù)、化學(xué)肥料價(jià)格指數(shù)、飼料價(jià)格指數(shù)的預(yù)測(cè)值如下：表5.10GM(1,1)模型預(yù)測(cè)換算結(jié)果單位：%年份農(nóng)資價(jià)格指數(shù)化肥價(jià)格指數(shù)飼料價(jià)格

11、指數(shù)200992.691.097.12010104.8102.8105.92011104.8102.8105.92012104.8102.8105.92013104.8102.8105.92014104.8102.8105.92015104.8102.8105.92016104.8102.8105.92017104.8102.8105.92018104.8102.8105.92019104.8102.8105.92020104.8102.8105.9圖5.1GM11模型預(yù)測(cè)結(jié)果圖農(nóng)資價(jià)格指數(shù)一一化肥價(jià)格指數(shù)一飼料價(jià)格指數(shù)附錄CM(1,1)模型模擬結(jié)果NZJGHXFL期數(shù)實(shí)際值模擬值殘差期數(shù)實(shí)際

12、值模擬值殘差199879.70-16.00-16.721998199872.71-9.09199983.53-5.67-6.361999199974.72-4.18200087.54L14L322000200076.79-0.01200191.744.945.70200120017&922.92200296.156.357.07200220028L115.412003100.778.679.412003200383.366.862004105.614.514.462004200485.674.372005110.682.582.39200520058&05-0.05200611

13、6.006.606.032006200690.492.492007121.571.27L062007200793.003.102008127.41-16.79-11.642008200895.58-12.32SL期數(shù)實(shí)際值模擬值殘差199871.69-16.21-18.44199975.93-4.87-6.03200080.423.023.90200185.176.97&91200290.206.80&16200395.537.43&442004101.18-0.72-0.712005107.16-0.34-0.322006113.49-1.794.412007120.

14、201.50L262008127.30-1L50-8.28NZJGDNZJGDDNZJGNullHypothesis:NZJGhasaunitrootExogenous:NoneLagLength:1(AutomaticbasedonSIC,MAXLAG=11)t-SlatisticProb?AugmentedDickey-Fullerteststatistic04843870.5029Testcriticalvalues:1%level2.5953405%level-1.94508110%level-1.614017MacKinnon(1996)one-sidedp-values.Augme

15、ntedDickey-FullerTestEquationDependentVariable:D(NZJG)Method:LeastSquaresDale:08/31/09Time;20:34Sample(adjusted);2003M032009M07Includedobservations:77afteradjustmentsVariableCoefficientStd.Errort-StatisticProb,XZJG(-I)-0.0006700,001384-0.4843870.6295D(NZJG(-1)0.6556820,0873467.5066840.0000R-squaredA

16、djusted R-squaredS E of regression Sum squared residLog likelihood Durbin-Watson stat0429121Mean dep endent var0.421509S D dependentvar1.311403Akaike info criterion128.9833Schwarz criterion-129.11951. 936552Hannan-Quinn enter.0.10519517242013.4057023.4665803. 430053NullHypothesis:D(NZJG)hasaunitroot

17、Exogenous:Nonet-StatisticProb?AugmentedDickey-Fullerteststatistic3.9485590.0001Testcriticalvalues:1%level2.595340LagLength:0(AutomaticbasedonSIC,MAXLAG=11)5% level10% level1.945081-1.614017*MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(NZJG,2)Method:LeastSqua

18、resDate:08/31/09Time;20:35Sample(adjusted);2003M032009M07Includedobservations;77afteradjustmentsVariablecStd.Errort-Coefficientr.StatisticProb,D(NZJG(-1)03429800,08686239485590.0002R-SQuared0J69859Meandependentvar-0.029870AdjustedR-squared0J69859SDdependentvar1432064SEofregression1.304783Akaikeinfoc

19、riterion3.382852Sumsquaredresid129.3868Schwarzcriterion3.413291LoglikelihoodDurbin-Watsonstat-129.23981.934426Hannan-Quinnenter.3.395027NullHypothesis:D(NZJG,2)hasaunitrootExogenous:NoneLagLength:1(AutomaticbasedonSIC,MAXLAG=11)t-StatisticProb?AugmentedDickey-Fullerteststatistic9.5992680.0000Testcri

20、ticalvalues:1%level2.5961605%level1.94519910%level1.613948*MacKinnon(1996)one-sidedp-values.AugmentedDickey-FullerTestEquationDependentVariable:D(NZJG,3)Method:LeastSquaresDale:08/31/09Time;20:36Sample(adjusted);2003M052009M07Includedobservations:75afteradjustmentsVariableCoefficientStd.Errort-Stati

21、sticProb,D(NZJG(-1),2)1.5468980,161147*9.5992680.0000D(NZJG(-1),3)0.3704290,1064843,4787210.0009R-SQuared0.630862Meandependentvar0.041333AdjustedR-squared0.625805SDdependentvar2J47223SE.ofregression1.313488Akaikeinfocriterion3.409554Sumsquaredresid125.9432Schwarzcriterion3.471353Loglikelihood125.858

22、3Hannan-Quinnenter.3.434229Durbin-Watsonstat2.099426Dale:08/31/09Time;20:51Sample;2003M012009M07Includedobservations:78AutocorrelationPartialCorrelationACPAGQ-SlatProb171.Igl10.6490.64934.1530.000n1-1-120.3890,05646.5920.000廣1r130.3700.24157.9650,000i+1-1-140.3680.07169.3540.000r1-1-150,2990.00676.9

23、760.000r1r.160.2730.08183.4230,000.r1-1-170,2180,06387.5990,0001111.180.1290.06689.0830.000-1.1190.0510.08089.3220,000-1.1-1-1100.0240,02989.3720,0001.1L1110147031291.3890.00011-11203310243101730.000“L1.r11302100.221105.960.000.1.1J.1140160-0J14108.460.000“L1-1-11502470,020114,480.000“L1-1-11603000.

24、021123.520,000“L1r.11702290.124128.900,000L1-1-11802180.006133,860.000“L1-1-11902430.032140,130,000“I.1J.12002580,073147.300,000“L11.1210268-0J06155J40.000“L1J.122-0,295-0.071164.830.000“I.1.*i12302440,150171,590,0001.1-1-12401710054174.970.0001.1r.12501200.182176.650.000T.1-1-12601120050178-160.000

25、T.1J.127-0J110082179.680.000.1.1-1-12800810.056180.500.0001-1-129-0,0900.033181.530,0001-1-13000830.048182.420,000-1.1-1-13100190.006182.460.000-1.1-1-1320.031-0.019182.590.000偏相關(guān)1階白相關(guān)4階拖尾ARMA(1,4)DNZJGCMA(l)MAMA(3)MAAR(1)DependentVariable:DNZJGMethod:LeastSquaresDate:08/31/09Time:21:15Sample(adjusted);2003M032009M07Includedobservations:77afteradjustmentsConvergenceachievedafter16iterationsMABackcasl:2002M112003M02VariableCoefficientStd.Errort-StatisticProb.C02713300-675130-0.4018